Some things you should know:
Japan/America and Europe use different TV systems (NTSC and PAL respectivelly). This matters, because video games must be adjusted for the different for the different formats. Because NTSC is a bigger market, games are usually adjusted for NTSC, and only a cheap PAL conversion is made, running in wrong speed (slower than it should) and with lower resolution (picture is letterboxed and "squeezed"). See comparison between NTSC and PAL here:
http://www.youtube.com/watch?v=ZmMXA7FpR_U
This was an issue all up until the PlayStation 2/GameCube/Xbox generation! For example, Final Fantasy X has a horrible PAL port (notice how the lipsynch is always good at the beginning of lines, but gets progressivelly worse the longer the conversation is...)
It is also an issue when playing Virtual Console/PSN games, see for example:
http://www.youtube.com/watch?v=T4gKOD4K088
So - which games should you play to get the best experience?
Portable consoles
Play anything, no difference in performance!
NES
Get an NTSC console and NTSC games. Most PAL games (with some exceptions) are horrible ports. A PAL console can easily be modified to be region free, but games will still run in the slower speed!
SNES
Get an NTSC console and NTSC games. Most PAL games (with some exceptions) are horrible ports. A converter can let you play most NTSC games on your PAL console - but the games will still run in the slower speed! If you're handy with a soldering iron, you could do this: http://www.gamesx.com/importmod/snes5060.htm - but remember that many games are "semi-ported" (for example, speed of music has been corrected but nothing more). Also, while the speed may be corrected for PAL games, you will still get a letterboxed and squashed video.
Nintendo GameCube
Sony PlayStation
Sony PlayStation 2
Get NTSC games, and any machine that can play NTSC games, if they run they will run properly (not including disc swap mods etc!) Many PAL games are bad ports.
Note that some NTSC PS2 games can even do 480p (as opposed to 480i)! This option is almost always removed in the PAL port.
Nintendo Wii
PAL ports of Wii games are fine. On Virtual Console, the "import" games are fine (including Final Fantasy VI and Super Mario RPG), they run in proper NTSC speed and resolution. Avoid all other games that can be purchased in the European VC store as they are the same shitty PAL ports as when they were originally released. Try to get games from a store in an NTSC region instead. TurboGraphx games found in the VC store are always fine, that console were built so that games did not have to be adjusted for NTSC/PAL!
Sony PlayStation 3
For physical PS1 and PS2 games, see above (get NTSC games). NTSC/PAL is no longer something to care about on PS3 games, and PS3 games are region free (all PS3 games works on all PS3 consoles). The PS1 games found in the european PlayStation Stores are bad ports. From any console you can, however, access any store, just lie about which country you live in, but NTSC PS1 games MAY not play on a PAL machine or vice versa (when launching it, you may get an "invalid video mode" message).
Notes:
- For consoles not listed, I don't know.
- There are no one NTSC region - Japanese NTSC consoles wont run north american NTSC games.
- Regardless of console, viewing NTSC signal may may require certain cables. Component and RGB has a higher probability of working with most TVs than the common composite and RF cables.
