This is what I can think of thumbing through the atlas on which I highlight these things. I don't count "clinches" when I was one year old riding with my parents when we moved from Texas to Virginia because I have no memory of it.
Virginia: I-264 (clinched part of it before it became an Interstate, but I count it anyway), I-664, I-66, I-81, I-581, I-85, I-95, I-395, I-495, US-29, US-50, US-211, VA-7, VA-9, VA-20, VA-28, VA-110, VA-193, VA-195, VA-234, VA-235, VA-236, VA-237, VA-267, VA-286, VA-289, VA-294 (before the number was changed, however), VA-309, VA-400, VA-401, unsigned VA-420, VA-895, Dulles Access Road, George Washington Memorial Parkway, Colonial Parkway; all sorts of secondary routes I won't even attempt to catalog; possibly VA-302 (VDOT-maintained roads on the UVA Grounds, but I don't know for sure which roads those are); I'm sure there are plenty of other primary routes I'm forgetting
District of Columbia: I won't even try to inventory the various streets. I-95, I-295, I-395, I-695, DC-295, the Whitehurst Freeway, Rock Creek Parkway, and I don't feel like taking the time to plot out the routes of the various US routes to figure out which of those I've clinched.
Maryland: I-68, I-70, former I-170, I-270, I-370, I-81, I-95, I-295, I-395, I-495, unsigned I-595, I-695, I-895, US-15, US-29, US-219, US-220, US-301, US-340, MD-3, MD-4, MD-5, MD-210, MD-200, MD-228, MD-295 (and the Baltimore–Washington Parkway to the extent they might not have overlapped at any given time), possibly some others whose numbers I don't know (particularly as to the Eastern Shore since I don't go over there all that often)
North Carolina: I-77, I-277, I-85, I-95, I-240, I-440, Green I-40 (Winston-Salem), NC-168; I had NC-147 clinched when I was attending Duke but the clinch was lost due to the recent extension. Might be some other numbered routes in the Raleigh–Durham–Chapel Hill area that I don't remember.
South Carolina: I-20, Green I-20, I-77, I-85 (both old and new routings in Spartanburg), I-95
Georgia: I-85, I-95
Florida: I-4, I-110, I-295, I-395, FL-417, FL-528, US-29
Alabama: I-10, I-85; don't remember the numbers for the state routes around Montgomery to know whether I clinched anything during the summer I lived there.
Mississippi: I-10, I-110
Tennessee: I-81
West Virginia: I-68, I-81, US-340, US-522, WV-9 (old alignment east of Charles Town, so I guess I have to re-clinch), WV-32, WV-93
Delaware: I-95, I-295, I-495, US-301, I think DE-404
Pennsylvania: I-76, I-176, I-276, I-78 (new alignment), I-81, I-83, I-95, US-15, PA-33, PA-283
New Jersey: I-76, I-676, I-278, I-95, I-195, I-295, Garden State Parkway, Atlantic City Expressway, Palisades Parkway; I guess I can't list the Turnpike because I've never clinched the Newark Bay Extension.
New York: I-278, unsigned I-478, I-678, I-81, I-190, I-95, I-695, US-15, NY-440, NY-878, Belt Parkway (I count the Cross Island Parkway as part of the Belt Parkway), Hutchinson River Parkway, Palisades Parkway, Garden State Parkway extension
Connecticut: I-84 (including after the I-86 era ended), I-86 when it was signed, I-95, Merritt Parkway, Wilbur Cross Parkway
Massachusetts: I-84, I-86 when it was signed; I-290; don't know the state route numbers well enough to be sure of anything else
New Hampshire: I-95
Maine: I-295 (clinched when it was numbered I-95), old I-495, new I-495 (clinched when it was numbered I-95), I think US-302, ME-3, ME-102, ME-189
Hawaii: HI-51, HI-58, HI-56, HI-520, HI-530, HI-550, HI-552, HI-560
Ontario: ON-137, ON-144, ON-400, ON-416, QEW, Don Valley Parkway, Gardiner Expressway
Quebec: Autoroute 5, Autoroute 15, Route 170, Route 323; not sure about route numbering to know for sure about any others, plus my most extensive travel through the province was almost 30 years ago (more recent trips have been ski trips and so were more limited)
New Brunswick: NB-114, NB-172, NB-772; lost a couple of clinches due to road extensions and realignments (I had NB-16 clinched in the days of the PEI ferry, but have not been back there since 1989)
Prince Edward Island: PEI-19, PEI-19A; don't know the route numbering/street names in Charlottetown to be sure of anything else (my sole trip to PEI was for the 1989 Canadian Boy Scout Jamboree and my focus wasn't on the roads)
Nova Scotia: NS-105, NS-106, NS-118, Trunk 6, Trunk 22, Route 333, the Cabot Trail, the Ceilidh Trail
States/provinces visited but with no clinches: Vermont, Louisiana, Texas, Ohio, Michigan, Illinois, Minnesota, Colorado, Wyoming, Idaho, Alaska, British Columbia, Newfoundland; I don't count Arkansas for the reason mentioned at the beginning of this post and I don't count Utah because I was only in the state for about 20 minutes changing planes in Salt Lake City.
(edited because I forgot about West Virginia)