Yep, until today, I didn't have a hard drive for my 360. In my opinion there was no need, I don't play online and I had 256MB of memory with the arcade pack I bought, it was plenty for save games. That all seemed to change when my 360 came up with a read error. I keep my discs clean, but it might have been the extreme heat and length of time it was on, which cause it.
Another factor is the noise from the DVD drive, it's pretty loud, don't you think? While the PS3 is almost silent, the 360 sounds like a mini lawnmower. It's loudest when it's loading data off the disc at full speed. It started to annoy me while playing Guitar Hero, it's distracting and doesn't make the music sound better. Then I heard that with a hard drive you can install the whole game from the disc and it the 360 reads it off the hard drive.
There, I kill two birds with one stone. By installing the games onto the hard drive, I'll be saving the lens of the DVD drive, and yes, they do wear out over time. Instead of the drive reading the disc for hours on end, I just need to install the current game I'm playing and after it copies the files to the hard drive, I only need to insert the game disc into the drive to start the game. Once I've booted up the game though, the drive is silent and the disc is never read. It's excellent, you'll be surprised by how quiet the 360 is without the DVD drive going nuts. But not only that, the game was loading much faster, bonus!
The game I installed took up about 5gb, so it's best to get at least a 60GB HDD or higher if possible, but of course a 20GB one will suffice for two or three games. Did I mention that installation is quite quick too? It's a very nice feature on the Xbox 360