Types of Clinches you have Clinched

[yakra]

Maine State Highways in New Hampshire
New Hampshire State Highways in Maine
New York State Highways in Pennsylvania

[corco]

Wyoming State Highways in Colorado
Montana State Highways in Wyoming
Montana State Highways in Idaho
Saskatchewan Provincial Highways in Alberta

Washington State Highways in Washington
Wyoming State Highways in Wyoming
Arizona State Highways in Arizona

Every mile of county road in Powell County, Montana

[oscar]

Manitoba Provincial Roads in Saskatchewan
Northwest Territorial Highways in Alberta
Yukon Territorial Highways in British Columbia
British Columbia provincial routes in the Yukon
Minnesota State Highways in Wisconsin

Hawaii state routes in Hawaii
Northwest Territorial Highways in the Northwest Territories (for now, additional mileage in progress)
Ontario and Nova Scotia Provincial Freeways in their respective provinces (also moving targets)
District of Columbia numbered district highways (duh, me and a zillion other people have all 4.3 miles)

[Takumi]

State primary highways in Chesterfield County, Virginia
Ferry routes on VA 31
Ferries in Currituck County, NC

[Alps]

One that doesn't usually get credit: every street in Livingston, NJ. (I biked as a teen.)

[cpzilliacus]

State primary highways in Chesterfield County, Virginia
Ferry routes on VA 31
Ferries in Currituck County, NC

White's Ferry between Montgomery County, Md. and Loudoun County, Va.

[hbelkins]

All Ohio River crossings between Kentucky and northern border states (bridges and ferries).

US routes in Kentucky that officially do not enter Kentucky.

West Virginia single-digit state routes that are not signed.

[CNGL-Leudimin]

As always, I come up with exotic stuff:
Catalan secondary highways in Aragon.
Toll-free motorways (i.e. expressways) in Guadalajara, Teruel and Zaragoza provinces. Surprisingly, I haven't clinched all toll-free expressways in Aragon since I have 3 miles of A-2 around Fraga still missing.

District of Columbia numbered district highways (duh, me and a zillion other people have all 4.3 miles)

Not me...

[SD Mapman]

US highways in Lawrence, Pennington, and a lot of East River Counties
All streets in Spearfish
Every bridge over the Redwater River and Spearfish Creek in Lawrence County

[hotdogPi]

Ramps getting on and off MA 213

[Eth]

US highways in Alaska.

More seriously:

Interstates in Delaware
Numbered routes of all varieties in the District of Columbia
The state highway network in nine Georgia counties (Butts, Clayton, DeKalb, Henry, Jasper, Newton, Rockdale, Spalding, Walton) (and about a mile short of also having Fayette)
(Also about a mile short of having Interstates in Maryland - just missing that little piece of I-70 west of I-68)

[Molandfreak]

Minnesota state highways in Wisconsin
Minnesota-Wisconsin bridges
Minnesota Interstates
Minnesota Freeways
South Dakota Interstates
South Dakota Freeways
Nebraska Interstates
Nebraska Freeways
Iowa Interstates
Rice County highways in Dakota County, Minnesota.
Discontiguous county roads in Houston County, Minnesota
County roads with both ends at the Minnesota border in Allamakee County, Iowa

[Takumi]

Spurs of US 60 in Nottoway County, VA
Generations of Honda Prelude found in the junkyard (hey, the OP never said it had to be a road-related clinch!)
State highways that connect to the Colonial Parkway
Interstates in Hampton Roads

[DandyDan]

All Iowa highways west of the Missouri River. 

More seriously, all Iowa Interstates, all Iowa-Nebraska toll bridges and all Illinois toll roads.

[dgolub]

All county routes in Connecticut, Rhode Island, and Massachusetts.  Also all county routes in New York City, all US routes on Long Island, and all interstates on Cape Cod.

Seriously:
* All East River bridges
* All Hudson River tunnels
* All New Jersey state routes in Pennsylvania

I'm not sure that I've ever clinched the entirety of a route system, although I'm pretty close to having all the county routes in Nassau County.  Just missing CR 7B, CR 55, CR 75, and CR 110, unless I'm forgetting something.  I've also been on all the interstates in New Jersey, except I-76 and I-195 (although I've been on I-76 in Pennsylvania).

[formulanone]

A quite lousy list.

- All the current 800-series State Roads in Florida
- All state-maintained tunnels in Florida and Alabama
- All mileage maintained simultaneously by both Arkansas and Oklahoma
- Former Grand Prix circuits on public roads held in Michigan
- Specifically not clinching Clinch County, Georgia

[roadman65]

Clinching every interchange ramp in the large Woodbridge Tangle in New Jersey.   It took me until after I moved to Florida to use the last ramp of it I missed while residing in the Garden State that is from NB US 9/ NB GSP to NJ 440 WB (yeah I know its now SB and has been for over 25 years, but to me the Middlessex County part of NJ 440 is still E-W).

This makes you actually think of how many local roads you can miss even if you see them with your naked eye on everyday travels.  It is just that I had no reason to go between the two in my travels.

I did though conquer every ramp and roadway inside the Newark Airport Tangle.  Most I done after receiving my drivers license just for the sake of driving through it then.

[Alps]

I'm not sure that I've ever clinched the entirety of a route system, although I'm pretty close to having all the county routes in Nassau County.  Just missing CR 7B, CR 55, CR 75, and CR 110, unless I'm forgetting something.

You are forgetting the vast myriad of alphanumeric county routes, inventoried by street name (I believe from A1 through E67 or thereabouts).