What activities destroy the ecosystem?

Lots. That's really a vague question. To give you a few broad ones:
1) Emitting gross amounts of CO2
2) Simultaneously destroying the trees (which convert CO2 into O2 [breathable air])
3) Stepping on every ant at the same time...for many reasons
4) Dropping a Nuke on Russia....duh
5) Joining Sarah Palin on a Moose Hunting mission from a helecopter
a) The helicopter's emissions are evil to the Earth
b) that moose was probably going to stampede some crazy Canadian lumberjack who is now going to kill a tree (See #2)
6) Killing all of the fish
7) Digging a trench that separates Europe and Asia
8) Lighting coal on fire
9) Chuck Norris
10) Using electricity that is made from non-renewable resources
a) Coal power
b) Oil power
11) Really, anything nuke-like.
a) Nuclear reactor plants
b) Nuclear Missiles
c) Some robots
d) Some theoretical space-ships
12) Excessive use of methane
13) Excessive use of oil
14) Deep water drilling for oil
a) it means we pollute underwater
i) double whammy!
b) We probably suck up, grind, and systematically kill some fishies
c) We inevitably leak some oil into the habitat
i) oil kills underwater plant-life
ii) fish die w/o that plant life
15) Zombie Apocalypses.