The short version is that the more creatures you have on your map, the slower things will be. Moving creatures take up more than idle creatures since the game has to compute and monitor path finding information for them, but all creatures contribute.
Items have a secondary effect: the more you have the slower the game goes. You have to get very, very large numbers of items to start noticing a big impact from them though. Regardless, many players, myself included, try to destroy or trade away useless items (like invader clothing).
Liquid flows can contribute a lot to slowdown. This includes moving water and magma / lava, but it's an especially big problem if it's spreading out, filling something or moving across z-levels (such as water falls). I believe the game is optimized to prevent most of the computations if it's an uninterrupted river moving to a map edge.
Finally, having a large map in any dimension (even z-levels) can slow the game down quite a bit. This is for various reasons, such as the caverns contributing to the above problems, but temperature calculations and various other tile related calculations will get slower with a larger map. I believe this primarily matters if you have lots of unrevealed tiles, since I think the game keeps unrevealed sections of the map abstract until it needs to load them for the more complex calculations.