PA <> NY thousands of times while working. There’s an asphalt plant (76 36 59.3 w 42 00 01.9 n) where the QC lab was just a few feet over the border in PA, but the pile the samples got dumped on when testing was finished was out the back door in NY. If you punch the above coordinates into google maps satellite pix, the arrow will point toward the building. Notice the border almost, but doesn’t quite touch the building. There must have been good reason to step across the line dozens of times a day.
We crossed the Ohio-Pennsylvania line enough times when I was a kid that we probably stopped at least once to pose for a picture by the “Welcome to [Ohio/Pennsylvania]” sign, though I don’t remember it specifically. I’m pretty sure we did the same at the 45th parallel sign on the way into Yellowstone (the Montana-Wyoming border), too, and we might also have on the Ohio-Michigan border, too.
Like many others, I’ve been to Four Corners, and stood in four states at once.
I’m pretty sure I’ve crossed the Friendship Bridge at Niagara Falls on foot at least once, for the US-Canada border.
And I’ve walked across the US-Mexico border at Brownsville, Texas.
Mexico into Guatemala and back, in the middle of the freakin’ jungle, within a 2-full-day trek. We were only in Guatemala for a few minutes, though. I was accompanying a group of indigenous landowners along a distant corner of the Calakmul Biosphere Reserve, about twenty km from the end of the nearest dirt road.
Quebec-Ontario, many times.
Quebec-Vermont, although I don’t know if I was on my bike or off it at the time.
St. Gallen-Thurgau in Switzerland (I’ve taken a walk specifically for that purpose).
I’ve taken a walk in Poland a few metres from Slovakia, and in Alberta two or three kilometres from Montana, but I didn’t cross the border.
I don’t know if I’ve actually been on Vatican territory. I’ve been on St. Peter place, but too late to actually visit the Vatican, so I stayed in the courtyard.
Crossed the Cambodia/Laos border today by bus and foot. Not sure exactly where the border was. If I had read this thread earlier I would have gotten out of the bus for the entire crossing.
China/Vietnam from Dongxing to Mong Cai. Walked over a bridge.
Entered and exited Hong Kong and Macau by foot a few times.
Crossed the Vietnam/Cambodia border by foot and on by motorbike. Not sure if I was on foot for the actual crossing.
US/Mexico at El Paso and Juarez. Walked over a bridge and thirty minutes later walked back.
US-Mexico at San Diego-Tijuana border station.
IN-MI at several places around Elkhart, IN.
IN-MI-OH near Angola IN.
TN-KY-VA in Cumberland Gap National Park
TN-NC in Smoky Mountain National Park
NC-VA many times and many places near Suffolk and Chesapeake, VA
On foot:
Italy -> Slovenia
Croatia -> Hungary
Hungary -> Slovakia
Slovakia -> Poland
Hungary -> Austria (accidentally. We were in a forest in Hungary, then somehow ended up on the other side of the border, judging by the signage.)
There’s also divided towns in Croatia and Bosnia, where one side was controlled by one group, and the other side by another, if you want to count that, and the locals could not generally cross from one side to the other.
In the US, I have no idea. I did the four corners thing, and I’ve walked NY->NJ, but there must be others I’m forgetting.
I’ve done DC/MD and DC/VA several times. Also the 4 Corners, AZ/UT/CO/NM a couple of times.
Italy/Vatican City, once.
US/Canada, once at Niagara and once somewhere in the Thousand Islands.
Would England/Scotland count, since they’re both UK?
The only one I’m certain of is Tennessee-North Carolina in the Smoky Mountains. I remember a family picture with me standing right at the sign.
When I was little we also took a little side trip into Tijuana from San Diego. I seem to remember us driving across the border, but I think most rental car companies don’t let you cross into Mexico, so it’s very possible we walked.
I can’t remember any specific instance, but I must have walked across the Maryland-DC border at some point.
NY > Ontario, here
While the bridges from the U.S mainland to Wellesley Island, and from Mary Island, Ont. to the Canadian mainland are large beautiful suspension bridges, the actual international bridge is a 90-foot truss across International Rift, the narrow strait separating Wellesley and Mary Islands.
Nevada- Arizona a bunch of times.
Waloked across the Mackinac bridge from the LP of Mich to the UP twice.
I’ve crossed the Rainbow Bridge at Niagara Falls on foot many times (Canada-USA; more specifically, Ontario-New York State).
I’ve also been on foot between Italy and Vatican City.
In a twist on the OP, I’ve pulled over on Highway 17 in northern Ontario at 90 degrees W. This is the border between Eastern time and Central time (Ontario has two time zones), and there is a sign and a pullout/picnic/rest area by the highway. I parked, read the plaques, and in doing so, crossed the 90 degree W time zone “border” more than a few times on foot.
Surprised nobody from the Kansas City area except Baker mentioned walking across State Line Road (Missouri-Kansas), or nobody from Chicagoland crossing State Line Road (Illinois-Indiana).
Google Street View does some goofy things around state lines; addresses like Dyer, Illinois, Temperance, Ohio, Prairie Village, Missouri and the like.
Paraguay to Brazil and back.
Likewise people from Omaha not inclined to walk across the wide Missouri could simply take public transportation to Locust Street and walk into Iowa on dry land, Carter Lake IA being surrounded on three sides by the city of Omaha.
Also, about a 2 km hike across Hancock MD will take you into both Weswt Virginia and Pennsylvania.
Considering they are classed as countries rather than states, and everyone here is citing states, then I’d say emphatically yes.
I’ve skiid from France to Switzerland and back.
USA => Canada (underage drinking at Niagara)
China => Vietnam (train from Kunming, tracks didn’t extend into the country at the time)
Thailand => Malaysia (‘visa run’ to renew my term of stay; walked into Malaysia, round a hut and back out again)
Malaysia => Singapore (bus from Mersing, but had to walk through the border checkpoint)
Ahem. “Of” age drinking at Niagara. Only Americans would call it “underage,” and I know you are British. 
England - Wales
France - Switzerland (on skis)
Italy - Switzerland
Italy - Vatican
Norway - Finland
Poland - Slovakia
Thailand - Cambodia
Zimbabwe - Zambia (Victoria Falls)
I think that’s it.
British say ‘underage drinking’ too. Never heard ‘Of age drinking’.