If at first you don't succeed, cheat, repeat until caught, and then lie!
The graphics are very good (which you would expect from a next gen platform) but it's the extra abilities that really swayed me in forking out the money.
Rather than just a gaming device, which the PS1/2 were, the PS3 is more justly defined as a computer. You can install an OS on it (Various Linux distro's) and it allow you to do so much more.
Click on full article for more info on additional features it has / can have.
Some of the things I've currently got set up are listed below:
Wireless - It comes with in built wireless so can connect to your home network immediately
Media Server - You can set up a media server on your home PC them stream the videos / MP3s / Films / etc. to your TV.
Football - Watch football over the web when the matches are not on in the UK? Yes you can stream them over as well, although the picture quality will no doubt degrade when viewed on the bigger screen.
Web Browser - It comes with a web browser which allows you to access the Internet / youtube and even BBCs iPlayer to watch videos.
Online Play - Free online servers for games with multiplayer capabilities.
Online Store - With free downloads of demos / beta test games / interviews / etc.
Blue-Ray Player - The DVD format war was ended with Blue-Ray on top (for now at least) and the PS3 is currently the best (most updated) and cheapest BR player. As well as being able to play ordinary DVDs.
Wireless Controllers - The PS3 seems to really have gone the wireless way, with various extras all communicating with it via bluetooth. When you get the chance upgrade to Dual-shock as it really is far better, and the original ones just seem too light.
Upgrade ability - It contains an ordinary SATA 2.5 inch HDD (for UK 40GB), which is the standard HDD that laptops use, so readily available. Allowing you to easily increase the space required, while having USB ports on the PS3 for backing up beforehand.