The question is: WHAT do you want to record?
Consoles: you are stuck with trying to get a
Hauppauge HD PVR. It has it's own recording thingy.
PC: FRAPS or Camtasia Screen Recorder. Personally, I use FRAPS for everything. Camtasia when FRAPS can't be used on a game (Streets of Rage Remake) or it just doesn't cut it (Arcana Heart 3).
Game via emulator (NES, SNES, GBA, things of that nature): Well...the emulator. :3 This
site has emulators suitable for recording (and rerecording. In short: make a movie file, abuse savestates when you make an error).
As for editing: all you need is AviSynth (to make edits, like trimming), VirtualDub (to see changes), and MeGUI.
We are still waiting on a suitable Amiga AGA emulator with robust recording features before tackling such games.