Best: Fast Worker.
Yes, there are plenty of people like morss who don't like this one. Its uses aren't immediately apparent; combat UUs are simple, easily understood. In general, a fast worker helps when:
1> You want to move onto a hill, or into a forest/jungle. Primarily early-game, but don't discount this one in continent/archipelago maps, where you might find that some ignored island has the resources you need. The late-game benefit on Terra maps should be obvious.
1a> In my current game, I had a huge stretch of jungle separating me from my neighbor, and neither of us had any reason to remove it (or even build roads in it) until I invaded him. A fast worker makes clearing that go much faster.
1b> In Civ4 you no longer need to pack cities quite so close together, so you'll occasionally have dead tiles between cities. When a late-game resources pops up in those areas (coal or aluminum on hills, for instance), you save a turn.
2> Just before railroads, you'll be improving all over the fringes of a large empire. Being able to shuffle back and forth across road networks helps a lot; moving 9 tiles instead of 6 is nice, it's as if you had everything railroaded already.
3> Don't think of it purely as 2 moves vs. 3. Remember that to start a worker action you only need a fraction of a movement point remaining. So, let's say you're improving around one of your cities, and many tiles aren't roaded yet.
With an old Worker you could move along a road for 1 square (2 in the later eras), move off into a plains tile, and start an improvement. Any more road movement, or any rougher terrain in the off-road tile, and you'd have to wait a turn. With a Fast Worker, you could move up to 3 squares (FIVE in the later eras), go off-road, and still be able to start the next improvement. Considering the size of the area each city occupies, this situation actually comes up a LOT.
4> When I'm invading someone's land and capture their workers outside a city, I can get them safely back to my territory. Although, in Civ4 you can railroad in enemy territory as you attack (unlike in Civ3), so it's actually not a bad idea to keep a group of workers with your attack stacks, as long as you're careful.
Sure, none of these benefits are huge, but added up across a dozen workers over the course of an entire game, it's far more than any other UU gives you. When you play any other civ, count up how many times your workers ended a turn without being tasked to a job. It's pretty common, actually. But for India, it's far more rare. Back in Civ3, I modded in an "Engineer" unit in the industrial era (1/5/1, 75% worker speed, all terrain as roads). It filled the same sort of role, and it was incredibly useful. You wouldn't want all your workers to be like this, but there'd be enough times where it was needed that you'd be glad to have the capability.
Then there's the obsolescence issue. This unit NEVER goes obsolete, so you never have to alter your timing simply to make room for it, and no matter what type of map you're on or what your neighbors do, it'll still give you its benefits. For example, I was playing a game the other night as Catherine, whose UU is the Cossack (Cavalry). It's a very nice combat UU; power 18 instead of 15, with a nice additional +50% vs. mounted units. But, at the time I reached the tech for it, I was surrounded by friends. So, do you simply sit back and waste the UU, or do you attack in a situation you wouldn't have otherwise?
And since I like Spiritual civs and building Wonders, Gandhi's the obvious choice for me.
As for the rest:
I dislike Ancient combat UUs; in most cases, an early war just cripples your own economy. That being said, Keshiks kick some serious ass; the movement ability means NOWHERE is safe.
I dislike Industrial/Modern combat UUs (Germany, America, maybe Russia). By the time you get to them, the game's already decided militarily.
Resourceless UUs (like the Jaguar) are mediocre for a human player, but fantastic for AIs (who aren't as good at city placement or hooking up strategic resources). Although, most of these have some other perk in Civ4 (Camel Archers retreat, for instance).
Now personally, I wish each civ had two UUs, one combat and one noncombat. They could have things like:
> Fast settlers for an expansionist civ
> "Covered wagon" settlers that start a city at size 2
> Workers that can fight a bit, for the inevitable Norse civ
> Fast missionaries, or missionaries with an Inquisition ability, or missionaries that can fight
> Missionaries that don't require a monastery
> Invisible scouts that can enter enemy territory
Instead, India's the odd man out.