In many urban areas, it is basically NYC. Which is great, and makes getting around easy. But once you get farther out, things dry up fast. And a good comparison would actually be Amtrak and the like on the East Coast of the US. Considerably cheaper (I would guess, off the top of my head, 60% of the cost for a comparable trip). But much like with US trains, your savings are at a cost of time. And a lot of the time, those savings aren't particularly significant once you factor that in.
As someone who travels a lot for work, I didn't see a huge difference in how I approached things while working on budgets. Fly to major city nearby and then get a train/rent a car to go to a smaller town (if needed). The former was more of an option, which was nice, but the latter was a lot faster if there were a few connections. And even when there was the option to just do pure train, the amount of time versus savings wasn't worth it.
And for personal travel? Even then, a flight was a lot more logical and not a lot more expensive once I factored in vacation hours and the like to handle transit times.
In terms of cities? Yeah, we are horrible (although, the UK and Ireland is almost as crap as we are once you get out of London). In terms of general (inter)national travel? A car is a lot less required, but not to the extent that a lot of us would think.