Wyoming 230 (and other routes split by a neighboring state)

[texaskdog]

What about MN-23 which enters Wisconsin for a couple tenths of a mile after crossing the St Louis River south of Duluth. Yet it is maintained Minnesota DOT.

Perfect example! 

[1995hoo]

VA-311 crosses into West Virginia and becomes WV-311; it then crosses back into Virginia, maintaining the same number again, and later it crosses into West Virginia, again as WV-311, before ending at I-64 out near White Sulphur Springs (the town where the Greenbrier is located). But I have no idea whether there are mileposts on the road nor whether they're sequential. Each state maintains its own portion.

[formulanone]

Georgia State Road 94, by Florida SR 2 (which is also a two-parter).

[hbelkins]

Also in West Virginia: WV 46.

Also in Virginia: VA 102

[ftballfan]

Georgia State Road 94, by Florida SR 2 (which is also a two-parter).

Florida SR 2 is actually a three-parter, with at least one end of each segment being at the Georgia state line.

[NE2]

Florida SR 2 is actually a three-parter, with at least one end of each segment being at the Georgia state line.

No it's not; the east part is CR 2.

[formulanone]

...close enough, since most signed Florida county routes were just state routes that were decom'd for mileage sake.

[roadfro]

in somewhat related, yet more absurd, numbering schemes ... Nevada 266 enters California and becomes CA-266 ... wait, no, it becomes CA-168, which then turns into CA-266 about 5 miles later, and then CA-266 returns to Nevada to become NV-264. 

Actually, NV 266 goes west into California, immediately becomes CA 266, then the road curves north and reenters Nevada as NV 264. 168 ends at 266 in Fish Lake Valley.

[Sykotyk]

It's funny, I drove the eastern leg of WY-230 and never noticed that on my way down toward Rabbit Ears Pass.

[newyorker478]

I also believe I-86 dips into Pennsylvania for a short section near Waverly, but that's for like a few hundred feet.

edit:

I-684 also runs New York - Connecticut - New York for a minor distance.

Don't forget NY 120A that is on the same general neighborhood...it runs a short distance in Connecticut, but NYDOT is responsible for maintenance and upkeep

NY 120a straddles the CT border for 75% of its length...however it only dips in a few times, and is entirely NYSDOT maintaned and signed, save an accidental CT 120A shield at the Merrit Parkway exit.

[TheStranger]

in somewhat related, yet more absurd, numbering schemes ... Nevada 266 enters California and becomes CA-266 ... wait, no, it becomes CA-168, which then turns into CA-266 about 5 miles later, and then CA-266 returns to Nevada to become NV-264. 

Actually, NV 266 goes west into California, immediately becomes CA 266, then the road curves north and reenters Nevada as NV 264. 168 ends at 266 in Fish Lake Valley.

IIRC, 168 used to extend on one of the legs of 266 to the Nevada state line, until some time in the 1980s.