If a large creature dies, does its corpse still occupy a 10x10 area?
How does this affect movement and combat, specifically charging?
Since a helpless creature does not block movement, a corpse shouldn't normally impede movement either. However, if the DM judges that the creature is very large, it may count as an "obstacle", which would impede movement. From the SRD:
You can’t move through a square occupied by an opponent, unless the opponent is helpless. You can move through a square occupied by a helpless opponent without penalty. (Some creatures, particularly very large ones, may present an obstacle even when helpless. In such cases, each square you move through counts as 2 squares.)
If the DM rules that it is an obstacle, then the following rules apply:
Like difficult terrain, obstacles can hamper movement. If an obstacle hampers movement but doesn’t completely block it each obstructed square or obstacle between squares counts as 2 squares of movement. You must pay this cost to cross the barrier, in addition to the cost to move into the square on the other side. If you don’t have sufficient movement to cross the barrier and move into the square on the other side, you can’t cross the barrier. Some obstacles may also require a skill check to cross.
On the other hand, some obstacles block movement entirely. A character can’t move through a blocking obstacle.
Flying and incorporeal creatures can avoid most obstacles.
A creature's body would take up the same space as if the creature was prone, so it's reasonable to conclude that a corpse takes up the same space. Since obstacle-ness is at DM's discretion, it's possible for him to rule that only some squares of the corpse are obstacles. You must pay two squares of movement to move through one square deemed an obstacle. However, can't end your square on an obstacle, which means you cannot fight from it.
You can't run or charge across obstacles, due to this rule under Hampered Movement:
You can’t run or charge through any square that would hamper your movement.
I always consider squares with corpses in them to be difficult terrain, and if the creature is sizable enough (as adjudicated by me), to require a jump or climb check to bypass (or to go around...). Unless it's the PC who just killed it the swing before, in which case as a bonus for their awesomeness, I assume they were setting up their charge to the next guy as part of their skillful dispatch of this critter, and they can run on through without penalty.
There is no RAW on this, but in 3.5 we still have DMs.
Technically by the rules I believe this becomes difficult terrain, which should halve movement and prevent charging unless a PC has feats or magic items to overcome this. In our group, however, we have never subscribed to that rule and have usually always played that once a creature was dead, it no longer had any effect on the game. Not realistic, sure, but usually easier to deal with.
When I would DM, I wouldn't usually care for medium and smaller creatures. But for something with a 10' base, it varied by situation.