dtgreene: Because I feel like it, I am posting about what happens if you play an Ultima game on a computer that is much faster than those of the time it was written. Note that there are a few assumptions:
1. You are not intentionally slowing down the game. (In particular, if using DOSBox, the number of cycles should be fairly high; note that the GOG versions may have those cycles set to low numbers precisely to avoid the sort of issues mentioned in this post.)
2. You are playing the unmodified game. In particular, note that the various Upgrade mods out there typically at least attempt to fix these issues (by applying a frame limiter, for example).

Anyway:

Ultima 1 (1984 DOS version): The game is strictly turn-based and does not animate characters, so there isn't too much difference. The water animation will be very fast, and ranged attacks have much faster animation, but that's about it.

Ultima 2: The game will likely fail to load with a "Division by Zero" error. (I believe the game tries to calibrate itself to the machine's speed by determining how long it takes for a busy wait loop to finish, and doesn't expect it to run so fast that it takes 0 time according to the system clock.) If you get past this, the game is unplayably fast; you are given essentially no time to make a move before the game makes you pass your turn.

Ultima 3: The game seems to run reasonably, albeit with fast animations. The whirlpool moves in real time, and will therefore move way too fast, but that's the only gameplay issue.

Ultima 4: The moon phases change in real time, and a a result, will change really quickly, especially when using Ztats (for some reason). Otherwise, there aren't any issues other than animation speed. The balloon *might* be difficult to control, however.

Ultima 5: Animations will be fast, but the game otherwise seems to work fine. The only real-time element to the game is sailing after hoisting sails, but that doesn't feel unreasonably fast, and you technically never have to do that.

Ultima 6: Strictly turn-based, and I think the game is programmed to properly handle fast computers, anyway.

Ultima 7+ shouldn't have any issues on fast machines (other than the many bugs that are present in the game regardless of the computer they're played on).

suchiuomizu: Doesn't that description of Ultima 1 change once you get into space? I've done very little if any playing of that part of the game, but it does look so turn based. Or maybe it just looks that way from the little I've seen of it.

Charon121: Why not just use Exult? It fixes the performance issues (including the hidden ones, such as party members getting hungry minutes after a meal) and brings significant improvements – smoother scrolling, possibility of mods etc.

dtgreene: Exult isn't 100% faithful to the original in terms of game mechanics.

In particular, as of the last time I looked at the source code, they had HP and MP regeneration wrong.

Charon121: It's not? Well, for me, combat in this game is more of an afterthought. Odd design choices, awkward execution, annoying respawning as soon as you scroll the screen a little. Best to get it out of the way as quickly as possible. The real strength of Ultima 8 lies in exploration, dialogue and world-building.