From Saint Cad’s link I see that Idaho County, ID, is one such. Any others?
Yes, you receive fewer services in unincorporated areas, and yes, you pay less taxes.
There isn’t any city government at all and hence no city regulations or taxes. All the government in an unincorporated area is administered at the county level.
I could go into more detail but it might hijack the discussion.
You mean of where they don’t follow county lines?
Stanley County, SD and Sioux County, ND.
There’s also Cherry County, NE
Also the southern part of Malheur County in Oregon is Pacific, not Mountain time.
More about these anomalies are found here. There’s quite a few.
Two municipalities in Nevada adhere to Mountain time: Jackpot and West Wendover. Jackpot’s anomaly is “off the books”.
Jones County, SD used to have split time zones until a few years ago when they moved the Central Time Zone line further west to the county line.
It used to be that Indiana didn’t go on Daylight Saving, but Ohio did, so part of the year they had the same time, part not. Someone phoned a store, inquiring about hours open. Store said they were open 24 hours. Question: is that Indiana or Ohio time?
Saskatchewan is generally ahead of Alberta. 
Port authorities have no power to exercise jurisdiction over the citizens who inhabit them. They are not “of the people”.
Ninjad on Lloyd, but I was curious about time zones as Saskatchewan does not succumb to the bane of some’s existance, daylight savings time. Off to wiki:
So you’re really only ahead of Alberta for part of the year Northern Piper. Did I get that right? It’s so confusing.
AFAIK there’s some kind of local government for pretty much everywhere in the US outside of Alaska, but in an unincorporated area it might just be a county or township with very few powers. (Each state makes its own rules for what each type of local government can do, so there is no general rule for what a particular type of place can do.)
Also McKenzie and Dunn county in North Dakota. In most of the state, the dividing line between Mountain and Central time is the Missouri river (which is also usually a county line), but right before it gets to Montana for some reason it changes to the Little Missouri river which is a tiny little river.
21 Miles North of El Paso is Anthony Texas/New Mexico. Walk across the street and you’re in another state. Anthony, Tx was incorporated in 1952 and the schools are part of the Anthony (TX) Independent School District. Across the street Anthony NM incorporated in 2010 and the schools are part of the Gadston (NM) School District.
I used to travel for work right on the Indiana/Ohio border (Richmond, IN and New Paris, OH). The motel I always stayed in was technically in Ohio but it was RIGHT on the border meaning the state line and the time-zone division was in the parking lot. Those people were more obsessed with time accuracy than any other people I have ever met in my life. They didn’t use the standard terms like Eastern and Central time. It was always ‘Indiana time’ and ‘Ohio time’. Even signs and casual notices had it noted.
I never thought that much about time-zones until I worked there except for things like TV schedules. It somehow came up many times a day there even for mundane things. Every single reference to a time had to be clarified as to what the person really meant. I found it more amusing than irritating but it was definitely strange. There are streets in that immediate area that are exactly on the line and one set of neighbors may be operating an hour off from their neighbors.
Not quite what the OP is looking for, but Broomfield, Colorado, which is north of Denver, used to lie in four separate counties, Boulder, Adams, Jefferson, and Weld. They petitioned the state in 1998 to become a consolidated city-county government, and in 2001, Broomfield County became Colorado’s 64th county.
The entire city of Lloydminster is considered to be in both provinces at once, a situation called “condominim”[sup]1[/sup]. Not sure what happens when the laws of the two provinces conflict, but I’m sure they’ve worked out some compromise. Residents are considered to be citizens of both provinces for various adminsitrative purposes, notably getting in-province tuition at both provinces’ universities.
I think there’s something similar at Flin Flon on the other side of Saskatchewan. Most of Flin Flon is in Manitoba, but a small part on the south[sup]2[/sup] is in Sask. I don’t know the details, but I wouldn’t expect it to be the same as Lloydminster, since the situation isn’t nearly as symmetric.
[sup]1[/sup] I bet you thought “condominium” only meant an apartment that’s owned individually.
[sup]2[/sup] The border between Sask and Manitoba is north-south, but it has several east-west jags. Flin Flon is at one of these jags.
And of course, the line dividing Central and Mountain time is generally drawn down the borders of the states of New Mexico, Oklahoma, and Texas, but El Paso (and some of the immediate east) is in Mountain time. I think I may have technically changed time zones last time I drove from Carlsbad for a stretch there going through the Guadalupe Mountains towards El Paso on US-180 on my way back to Las Cruces but it’s not like there was anywhere to stop anyway.
Here’s a question that I’ve been curious about. Many (Most? All?) states require you to register your car in their state if you live there. There are also states that require you to register your car if you work in the state (Arizona is one). What happens if you live in one state and work in another and are required to register your car in both?
It is fairly common in some states for county lines to run through a city or town. As has already been mentioned, all units of local government (cities, towns, counties, etc.) are state creations, and in some states (at least) cities and counties perform such different functions that it wasn’t deemed necessary to require their boundaries to allign. That does tend to create some confusion, especially if you also factor in school districts (who’s boundaries may have little to do with city or county boundaries.)
I think its possible in theory, but there would be a lot of complications besides just “political resistance.” For example, each state has its own laws about exactly what powers local governments have and how they relate to the state goverment as well as other levels of local government (such as counties.) Part of the reason that there are no such multi-state municipalities may be that it is less of an administrative headache just to set up separate municipalities on each side of the state line.