If I lay three fire traps in the same place, and a mob steps on them, does he take 3x the DoT?
No, multiple instances of the burning ground damage from Fire Trap will NOT stack.
Only different sources of burning damage can stack. For example, an Ignite debuff from a spell's critical hit and the Fire Trap ground burn will stack.
When 2 of the same burning sources are present the highest damage source will take effect. Multiple effects can still apply, like 2 Ignites on one mob, but only the highest damage one will actually deal damage.
Once the highest damage effect ends, if another instance of that effect was applied and still has duration left, it will then do what damage it has left. This goes for Righteous Fire, Ignite, and Fire Trap's ground burn effect. Searing Bond, a recently added skill, is an exception and the beams can stack with itself.
This is why you should try to spread out Fire traps a little bit whenever possible.
Posted by Mark_GGG, PoE developer and creator of the games skills and their mechanics.
...Ignite, RF, ground fire and now Searing Bond are all separate sources of burning damage, and all stack. Ignite, RF and ground fire do not stack with themselves (only the highest of each takes effect at a time), but do with each other.
Searing bond beams stack.
As of Patch 1.0.5 Searing Bond Beams no longer stack.
The DoT of Firetrap is actually a fire-based health degeneration. So yes, health degeneration from all sources stacks. If you can tank strong monsters, a typical use is to spam firetraps under you so the enemy takes all possible damage.