2 Numbered Highways going between the same 2 points.

[mapman1071]

Arizona DOT does not allow 2 numbered highways to travel between 2 points.
Example: at one time AZ88 and US60 both roads traveled from Apache Junction to Miami today only US60 travels between these Cities, AZ88 ends at Roosevelt at Jct AZ188.

Other Examples
US60 & AZ260 Show Low To Springerville (260 now ends in Eager)
I-10 & AZ84 Downtown Casa Grande to Jct I-10, AZ 84, AZ87 (AZ84 Ends In Downtown Casa Grande at Jct AZ387 & AZ287)

Are there other states that have this rule?

[Mapmikey]

Not only does Virginia not have this absurd rule, they have twice had a situation where two different roads with the same number travel between two points:

US 360 and VA 360 from Danville to near Scottsburg (since 1984)
US 29 and VA 29 from Culpeper to Warrenton (1933-49)

Examples in Virginia that would violate Arizona's rule (which they violate with all its interstate business loops, US 60/I-10 and I-10/17)

US 1 and VA 2 (Richmond to Fredericksburg)
US 17 and VA 3 (Fredericksburg to Gloucester)
VA 3 and VA 200 (White Stone to Kilmarnock)
US 60 and VA 5 (Richmond to Williamsburg)
US 50 and VA 7 (Winchester to Falls Church)
US 60 and VA 13 (Cumberland CH to Powhatan CH)
US 15 and VA 20 (Dillwyn to Orange)
US 29 and VA 28 (Remington to Centreville)
I-64 and VA 33
US 11 and VA 37 in Winchester
US 460 and VA 40 (Blackstone to Waverly)
VA 57 and VA 457 in Martinsville
US 460 and VA 61 (Tazewell to Narrows)
VA 63 and VA 83
US 11 and VA 100
US 460 Bus and VA 111
US 421 and VA 113
US 11 and VA 117
US 501 and VA 129
US 460 Bus and VA 131
I-64 and VA 134
I-64 and VA 143
US 258 and VA 143
US 60 and VA 147
I-295 and VA 156
US 58 ALT and VA 158
US 1 and VA 161
I-95 and VA 161
US 29 Bus and VA 163
US 13 and VA 166
VA 165 and VA 168
I-64 and VA 168
several routes and VA 337
VA 3 and VA 205

There are probably more...

Mapmikey

[english si]

In the UK - A282 and M25 end on each other (M25 going the long way, A282 going the 5 mile way).

I don't think there's any other end-on-each-other where both routes start and end at the same point in the UK, but there's lots of roads that start and end on the same road (like old routes that have been bypassed) and perhaps a couple where road x starts on road y and road y then ends on road x. There's also things like the A41 and A5, which cross each other twice, and there's lots of cases where motorways will have several junctions with one road (IIRC the A38 and M5 share about 10 junctions)

[Revive 755]

Missouri
Doesn't appear to be such a rule

MO 30 and I-44:  From the I-55/Gravois interchange out to St. Clair.
I-64, US 40 and I-70:  From the west end of the PSB out to Wentzville
I-29/US 71 and US 169:  From north of downtown KC to St. Joesph
MO 5 and MO 87 between Booneville and Glasgow
MO 151 runs on what appears to be an old alignment of MO 22 just west of Centralia
MO 168 and US 61 from the north end of Hannibal to Palmyra

[TheStranger]

In California...

I-280 and US 101 between San Jose and San Francisco
Route 99 and I-5 between Wheeler Ridge and Sacramento
Route 60 and I-10 between Los Angeles and Beaumont
Route 154 and US 101 between Los Olivos and Santa Barbara
Route 85 and US 101 between south San Jose and Mountain View
Route 9 and Route 236 (former alignment of Route 9) north of Boulder Creek
Route 13 and I-580 between Oakland and Berkeley
Route 1 and US 101 along the coastline west of Ventura, and between Gaviota and Arroyo Grande, San Luis Obispo and San Francisco, and Marin City and Leggett
Route 33 and I-5 between I-5 Exit 349 and Exit 452

[hbelkins]

There are probably more...

Mapmikey

I was looking for US 460 and US 221.

[froggie]

I was looking for US 460 and US 221.

You won't find it.  Though they duplex between Roanoke and Bedford, they only meet that one time.  Not since 1975 (and that one only lasted 5 years) would US 221 and US 460 be on this list...

[Alps]

I'm pretty sure this list is not meant to include Interstates and their US/state route partner that they bypassed...
Back in the day, NJ 24 went west from Newark to Phillipsburg.  So did (and does) US 22.  Originally, both of these were the same caliber route, and US 22 was much shorter (and less mountainous).  Guess what - US 22 was improved (dualized, part of which eventually became I-78) and NJ 24 was truncated.

Both ends of NJ 36 are at NJ 35.  You'd never use 36 to connect them - it's a huge backwards C.  Even worse is NY 28, which once began at US 9W (at that time, US 9 was split into W and E) and also ends at US 9, and is a much huger C.  28 still begins and ends east of the Thruway (I-87) while spending most of its time to the west.

[jdb1234]

AL 119 and AL 25 both run from Montevallo to Leeds, but take different routes through Shelby County.

Also, Both US 31 and US 431 run from Franklin to Nashville, TN.

[hbelkins]

I was looking for US 460 and US 221.

You won't find it.  Though they duplex between Roanoke and Bedford, they only meet that one time.  Not since 1975 (and that one only lasted 5 years) would US 221 and US 460 be on this list...

I was interpreting "points" to mean towns, not specific intersection points; therefore I was thinking of those two between Bedford and Lynchburg.

[golden eagle]

I-20 and U.S. 80 run parallel with each other throughout central Mississippi.

[national highway 1]

AZ 66 and I-40 between Kingman & Ash Fork

[Brandon]

US-41 and M-26 between Copper Harbor and Hancock, Michigan
US-41, M-26, and M-203 between Calumet and Hancock, Michigan (how's that for three different routes!)
US-41 and M-35 between Menominee and Escanaba, Michigan and between Gladstone and Neguanee, Michigan
M-123 and M-28 between Newberry and Eckerman, Michigan
US-2 and M-69 between Crystal Falls and Bark River, Michigan
I-43 and US-41 between Milwaukee and Green Bay, Wisconsin
I-43 and WIS-57 between Saukville and Green Bay, Wisconsin
WIS-42 and WIS-57 between Sturgeon Bay and Sister Bay, Wisconsin
US-2 and WIS-13 between Superior and Ashland, Wsiconsin
I-94 and WIS-16 between Waukesha and Wisconsin Dells, Wisconsin
I-24 and US-45 between Vienna and Metropolis, Illinois
I-90 and US-12 between Maywood, Illinois and Madison, Wisconsin
I-94 and US-12 between Chicago, Illinois (95th St) and Lake Delton, Wisconsin
I-90 and US-14 between Janesville and LaCrosse, Wisconsin

An old set of now changed routes and even a decommissioned route,
US-66 (formerly IL-4) and IL-4A (now partly IL-171) between Chicago and Joliet, Illinois

A few parallel routes that may or may not count,
I-80 and US-6 from Davenport, IA to Lansing, IL
I-74 and US-150 from Moline to Danville, IL
I-39/US-51 and IL-251 from Kappa, IL to Beloit, WI
I-70 and US-40 from Troy, IL to Terre Haulte, IN
I-57 and US-45 from Effingham to Kankakee, IL

[TheStranger]

A couple of more California examples:

Route 158 and US 395 near June Lake
Route 36 and Route 172 (former segment of Route 36) between Mineral and Mill Creek
Route 193 and Route 49 between Auburn and Placerville
US 101 and Route 135 (former US 101) between Santa Maria and Los Alamos
Route 35 and Route 1 between San Francisco and Pacifica
Route 98 and I-8 between Ocotillo and I-8 Exit 143
Route 86 and 111 between Mecca and Heber
US 101 and Route 254 (former US 101) through Humboldt Redwoods State Park

Route 12 and Route 116 almost do this (but not quite, with a short segment of Route 121 between the two in Sonoma).  Another close-but-not-quite is Route 88 and Route 26 between Pioneer and Stockton, as well as I-10 and Route 111 between Cabazon and Indio.

[sandiaman]

Here  are some  routes that parelell  each other between  the same cities  in NM:

NM  14  and I 25, between Albuquerque  and Santa Fe
NM  1   and I-25  beteeen  Socorro and T or C
NM 2   and US 285  between Roswell and Artesia

[WNYroadgeek]

NY 5 and NY 33 parallel each other from Buffalo to Batavia.

[TheStranger]

One random example I happened upon looking through an atlas is US 371 and US 278 in southwest Arkansas, between Nashville and Rosston...

Another one I can think of is US 311 and US 220 between Madison and Randleman in North Carolina.

[bugo]

While not quite qualifying, the Muskogee Turnpike/Broken Arrow Expressway combo and US 64 both take different routes between Tulsa and Muskogee.

US 62 and 412 between Alpena, AR and Springdale, AR
US 64 and 412 in several places in OK
US 62 and 277 in southwest OK
US 59 and 71 between Acorn, AR and St Joseph, MO

[agentsteel53]

US 60 and 66 between Vinita, OK and Amarillo, TX and between Amarillo and the Four-Level Interchange in LA. 

[TheStranger]

For a current example...US 6 and 44 between I-384's terminus and Providence.  Another current example is Route 38 and Route 18 around Big Bear Lake, formerly Route 18 and 30.

Some historic examples:
I-10/US 70/99 and US 60 took different paths between Pomona and Beaumont (with 70 actually being north of 60 for that entire duration).

Another one: US 466 and US 66 between Barstow and Kingman (though IIRC, they never intersected in Barstow).

US 6 and US 66 between Joliet and the Four-Level Interchange in Los Angeles.

Route 30 and US 66 between San Dimas and San Bernardino.

Route 71 and Route 74 between Anza and Lake Elsinore.

Route 2 and US 66 between Hollywood and Cajon.

Route 18 and US 66/91 between Victorville and San Bernardino

Route 18 and US 395 between Mountain View Acres and San Bernardino

[agentsteel53]

Another one: US 466 and US 66 between Barstow and Kingman (though IIRC, they never intersected in Barstow).

that is correct.  They were about a mile apart in Barstow, separated by the US-91 (1st Ave) bridge across the railroad tracks and the Mojave river, which connected the 66/91 multiplex to the 91/466 multiplex.

speaking of 91 - US-6 and US-91 between Santaquin, UT (just south of Salt Lake City) and Long Beach.  

Given how US-6 ends up heading east to terminate at US-91, which is heading west, it would be quite impressive to renumber US-91 as US-6 and have it intersect itself in the Salt Lake City area before terminating at Sweetgrass, Montana, 5000 indirect miles away from Provincetown!  

[TheStranger]

And thanks to I-70, US 6 and US 50 now do this in Utah from Delta to Green River.

[mapman1071]

AZ 66 and I-40 between Kingman & Ash Fork

AZ66 Ends In Ash Fork 2 Blocks North Of I-40

[deathtopumpkins]

Mapmikey, I disagree on many of your Virginia examples. Quite a few of those route pairs may meet multiple times, but their primary destinations differ. For instance, I-64 and VA 134: They meet twice (and multiplex briefly) in Hampton, but 134 connects downtown Hampton with Yorktown VIA US 17, which I-64 arguably does not. Same for US 258 and VA 143: they share a common end at Fort Monroe, and cross each other again in Newport News, but 143 travels north from there to Williamsburg, while 258 travels south across the James River Bridge and into NC.

[huskeroadgeek]

I'm surprised nobody has brought up I-90 and I-94 yet. I don't know of any two interstates that meet together so many times while taking different routes in between. I-94 splits off of I-90 at Billings, MT, then they meet again at Tomah, WI and multpilex from there to Madison, split again, meet and multiplex through Chicago, then split off again and cross one final time in NW Indiana.

There are at least several instances of this in Nebraska. NE 1 begins and ends at US 34(the E. junction is actually US 34/75). NE 109 begins and ends at US 77(it is an old alignment of US 77). NE 12 splits off from US 20 W. of South Sioux City and ends in Valentine at US 83 about a 1/2 mile N. of US 20.
Also, US 6 and US 34 have a relationship kind of like I-90 and I-94. Going WB they sort of first meet in Lincoln-they don't directly meet as US 6 travels over the I-180/US 34 freeway without an interchange and access is provided at the Cornhusker Hwy. interchange just to the N. where US 6 is just a couple of blocks to the E and then take different routes to Hastings where they meet again. They are then multiplexed for a pretty long distance across southern Nebraska, splitting again W. of Culbertson. They almost meet again just E. of Brush, CO where US 6 joins up with I-76 and US 34 picks up BL I-76 through Brush and Ft. Morgan. Then W. of Ft. Morgan, US 34 joins with the I-76/US 6 multiplex for about 8 miles, splitting again finally when US 34 heads W. to Greeley and Estes Park while I-76 and US 6 continue SW to Denver.