Well, I recycle as well, but my goal is mainly to prevent my trash from winding up in a landfill.
As far as the trees, we're currently using more of them than we are replacing. The amount of forested area on the Earth is massive, so cutting down a tree or 100 or 1,000 trees doesn't seem like it makes any effect.
Over a 5 year period, we lose about 1% of our forested areas. This means an area previously listed as "forest" has to be reclassified as something else like plain, swamp, etc. That 1% is equal to 36 million hectares (about 89 million acres).
Considering the amount of CO2 we're putting out with cars, airplanes, etc. and considering that trees turn CO2 into oxygen, I don't think having less trees is a good idea.