Good question. IV, V, VI and VII are all so great.

My nostalgic side would probably say IV.

To replay them today I might say VI or VII since they've probably aged better.

V is really great too, but it doesn't have as much nostalgia factor for me since that is the only one that I didn't play back when it was new (I don't think I played it until perhaps after VI, but by them it seemed kinda dated so I never quite fell in love with it even though it was great).

Honestly, I couldn't get past the first town of U6. The small viewing area for the overworld was tolerable when it was zoomed out in prior games, but now that the overworld and towns/ dungeons are represented on the same scale, navigation quickly became infuriating. In between that and the needlessly complex magic system being bogged down by an awful inventory management interface, I ragequit at least half a dozen times over the period of a month.

From an overall design standpoint - strictly from how the game is put together - Ultima IV is probably the best. And the best around, too; no one has since built a game with that complex and intricate a morality system, despite how popular black-and-white morality systems have become, although Jeff Vogel of Spiderweb has put together some convincing imitations. I enjoy V more; it generates a much more threatening atmosphere, especially when you walk into a once-friendly town at night looking for a place to stay and all the trees are dead, the people won't talk to you / run away from you / steal your stuff / outright attack you, and there's this creepy shadowy humanoid figure passing through the walls to run you down. III is a good time, too.

My pick would be Ultima Underworld.

VII for me. Just a wonderful all-around game.

What about World of Ultima?

They're Ultima VI in other scenarios. If you like Ultima VI and Jules Verne, then you'll like Savage World and Martian Dreams as well.

Ultima VII still cannot be beat for creating a living, breathing world. In Ultima VII, you can use almost anything, people have schedules, and the world is alive. Forget about buying a sword after 6:00 PM or so. The shop dealers go to the pub for dinner and drinks, then they go home and sleep.
You don't have to kill for money. You can bake bread, help farm pumpkins, even act as Britannian Vice and sieze drugs to give them to the Royal Apothecary for money.
And you will care about each of the characters. There are also surprises. If you are playing it for the first time and you see a devilish-looking individual in the castle, do not attack! He is the Royal Advisor to Britannia and another is a member of the Council. This is the first utima since III in which there are non-human citizens of Britannia.
Yes, the two "devilish" individuals in the castles are gargoyles, and honored citizens of Britannia.
There is too much awesome in this game to list it here. It is the pinnacle of Ultima.

Ultima VII was my favorite game for a very long time. BG2 over took it, but only after the 3rd playthrough or so. Ultima V was always my favorite story though. Playing the Dungeon Siege remake of that was fantastic. Its really hard to say if V or VII were my favorite Ultima. No doubt that 7 is a much better game over all, but 5 will always have a special place.

Ultima 6. Good balance between combat, detailed world, npc depth, ect.

Yeah. For me its Ultima 6 too. For the same reason above.

With no nostalgia to attach to any of the games, I'd have to go with 5. While I think 6 and 7 are fantastic, I'm not a big fan of combat in either. 5's is far from perfect, but it's surprisingly deep for an Ultima game. I'm also impressed with how much story and complexity they got out of such limited space. Not having music in the DOS version is a bummer, but there's a patch for that.

7 is a very close second.

I would say my favourite is Ultima 8 for atmosphere, and Ultima 9 for atmosphere.

Haven't played them all but 6, and Worlds of Ultima 1 and 2