Homebrew PCBs

For SMT, what I do (if possible) is put the board back on the
hotplate.  Of course, this doesn't work if there are any parts on the
back, or PTH parts.

For most other cases, I use a Metcal Talon, but unless you can pick
one up on eBay (like I did :) it might be a bit pricey.  Talon in one
hand, tweezers in the other - pick the part off the board with the
Talon, then grab it with the tweezers to get it away from the talon.