Cataclysm (and DDA) has an interesting AP-like system. Entities are allotted moves according to their speed stat (can be modified, of course), and then act until their move score goes negative, at which point their turn is over, and it round-robbins through everything, though the player has a bit of special handling. Actions that take significantly more than a "turn" (100 moves) are pushed into a long-action system, where the player's turn is entirely consumed by burning down the balance of the long term action, once it reaches 0 the action completes, and it's now the player's turn (usually with a small balance to act with). Actions that take a little over 100 moves take the entities balance negative, and can leave them spending several turns to go positive again, especially if they are slow for some reason.
It's not a system that's very good for players to try to interact with directly, because the details of the system aren't particularly legible to the player. We do have a UI element that indicates how many moves the previous action consumed, but the player's position in the turn sequence is entirely illegible. Another shortcoming with respect to highly tactical play is that we don't provide any animation delay for monster moves, all monster actions happen in a single screen refresh unless they trigger an animation effect, such as by hitting the player. It would be totally impractical otherwise as we can have 100s to 1,000s of monsters onscreen at once. On the plus side that means you can run from a very large horde at a high turns/second rate, which would otherwise be quite frustrating when trying to outdistance pursuers over open ground.
Also some interactions, like vehicle movement, can have several animation ticks per action, a vehicle can easily move up to 6 squares a turn, and extreme vehicles can move dozens of squares per turn.
