Backwards Compatibility

Backwards compatibility--the ability to play games from an older version of a console on its newest version. For example, you bought a Nintendo Wii. The Wii can play all of the games a Nintendo Gamecube (Nintendo's previous system) could play. So the Wii is backwards compatible with Gamecube games.

However, the Nintendo64 (N64) was Nintendo's system before the Gamecube. You cannot play N64 games on the Gamecube. Therefore, the Gamecube is not backwards compatible with N64 games.

"Backward compatibility is a nice secondary consideration, but it's far from the number-one priority."
Jack Tretton, president of Sony Computer Entertainment America, from an article on Reuters when talking about the release of the 40GB PS3, which is not backwards compatible with PS2 games

While backwards compatibility, in this case the ability to play PS1/PS2 games on the PS3, isn't the number-one priority when creating your next-gen console, I think it's pretty important for one HUGE reason that tugs at the heartstrings of gamers everywhere:

Nostalgia.

When I found out my old GameBoy and GameBoy Color games wouldn't be able to play on the new-fangled Nintendo DS, I was heartbroken. I was over it in about 15 seconds, but still--if I wanted to play through Zelda: Link's Awakening, PokeMon Pinball, Wario Land: Super Mario Land 3, I would have to keep my older GameBoys in reach. This can be a hassle, and a danger to the older handheld systems I'm trying to preserve and keep in working condition (which is surprisingly difficult over a 10-year span).

And the Playstation 2 has some truly incredible and now comparatively inexpensive games, especially if you hunt the used games sections. It's almost a waste for Sony to just turn their backs on this.

Then again, Sony's PS3 has been in the red for quite some time, and from what I hear has a long road to recovery. Opting out of completely working backwards compatibility probably help them cut a little bit of production cost off the PS3.

Wii, DS, Xbox 360, PS3 backwards compatibility

The Nintendo Wii can play all Gamecube games. Cannot play N64 cartridge games.

The Nintendo Dual Screen (NDS) can play all GameBoy Advance games. Cannot play GameBoy or GameBoy Color games.

Sony's 40GB PS3 can only play Playstation 1 games.
Sony's discontinued 60GB PS3 could play most PS2/PS1 games.
The 80GB PS3 can play an assortment of PS2 games, and PS1 games.
Go here to find out if your PS2 titles are compatible with your PS3: Sony's PS3 Compatibility Status.

Microsoft's Xbox 360 also lacks complete backwards compatibility. Here is Microsoft's official list of Xbox games compatible with the Xbox 360 and official backwards compatibility FAQ.