Can you play PlayStation 1 games on the PlayStation 3?

Just out of curiosity, can you play PlayStation 1 games on the PlayStation 3? If so, how does it deal with save games? Does it have a connection for old PS1 memory cards or does it save them to the hard drive (the PS3 has a hard drive, right)?

Yes, all models of the PS3 are backwards compatible with the PS1. Only some models are backwards compatible with the PS2.

You can save your games to the PS3 HDD, or (if you need to import old saved games) you can buy an adapter.

The adapter costs about $30 and is available on Amazon:
http://www.amazon.com/PlayStation-3-Memory-Card-Adaptor/dp/B000K1GZIU

Yes, all PS1 games (with very few exceptions) can be played on the PS3.

If you want to save, you can buy an adapter which allows the PS1 memory cards to be used, or you can create virtual memory cards on the PS3 Hard drive.