First off I'll warn that this is long but I would really appreciate some help...

Things haven't been going well for my PS3 over the last week. Last Friday I was playing some Red Dead Redemption online and things were going smoothly until after finishing a hideout, the game froze on me. This sort of thing had happened before so I thought nothing of it. But powering it down normally didn't work at all so I had to flip the switch on the back. I've had to do that before so, again it didn't bother me much. Later that day, I was playing some Modnation Racers and was hanging in the Modspot with my Nabooru mod, just doing nothing and my game freezes again. Same story and I had to flip the switch off the back.

Then I had no real problems until two days ago. I was playing Rock Band 2 and was in the Character Shop when the game semi-freezes. The character is still moving and the music is still fine but my buttons don't work and the game won't quit itself. The clothes names scroll while I shop but the image doesn't. This weirded me out enough but I flipped the switch and tried again with little problem, except for when I tried to boot up Rock Band 2 right after. The PS3 wouldn't even get me into the game. Today I picked up Lego Harry Potter and was playing it and enjoying it. Things were going smoothly until it froze hard again. Luckily I was about done with it for the time being as the family wanted to play some Rock Band. So I put Rock Band 2 in again and we were playing for a good half hour until the game freezes on me right in the middle of a song and starts skipping Give It Away like a record. I had to flip the switch and hard power it down again.

Suffice it to say I'm really concerned about my Playstation. I've had it since 2007. It's a 60 GB model and has been a great device. It shows no other problems. It plays videos and music on the system and I've been playing a PS2 game on it over the last week with no freezing or problems. The only problems seem to occur when I'm playing games but it seems almost random.

Same thing happened to mine 2 weeks ago!  it would feeze constantly then after three weeks it just displayed a yellow light when i turned it on meaning its a dead  system.  Sorry to lay the bad news but if its like mine it will die within a week or two!  I recommend u backup ur data while u can!!

How do I backup my data? Is there an easy way to transfer save data, game data, and most importantly trophies to a new PS3?
 
This is really sad. I've never had a system die on me before... My Genesis, SNES, N64, Cube, PS2 and handhelds have all worked fine and still work to this very day. My poor PS3 dies in 3 years.

The launch 60 gig that I bought recently freezes sometimes.  Oh well, if it ylod or another common break I know a good place that should be able to fix it for about $120.  

That's harsh dude. Sorry to see that your system is failing. Especially a launch model. Well, just back up your data for now, deauthorize you playstation, and try reformating the hard drive. Basically re-installing the playstation OS.

you can backup your saves I think with a usb flash drive or external hdd

Thanks again for all the helpful advice everyone. Let's say I don't have an external hdd. What kind would you recommend I pick up? I could use it to backup my data for my PS3 and also my laptop. Any particularly good brands or sizes?

A good size 500gb would be good and a 1tb should cover everything in your house
I would suggest you buy a Seagate or WD hdd
here is example of a good one 
1TB

Do you have any Blu-Ray movies/does it play them normally?  You wrote that it plays PS2 games just fine so maybe its just your Blu-Ray diode failing.  If that's the case you can find disc drives on ebay and there are guides on youtube for replacing them.

i think you should call up sony to get them to fix it. you can get your saves back from getting a flash drive and saving them there.

Okay, so I ordered an external HDD from Amazon and now I have it in my hands... But I'm not exactly sure what to do next. I don't want to mess anything up... Is there any way I could get a simple (yet detailed-ish) step by step guide to what I'm supposed to do now?
 
Thanks again.

Bump... Anyone?

My suggestion would be to vacuum the vents. Also if you know someone who can reapply thermal paste to the inner components that would help.

I have both vacuumed and cleaned the vents with canned air but to no real avail. :/
 
EDIT: Okay I have my HDD connected to the PS3 and it's backing up as we speak. What should I do once that is finished? 
Please forgive my lack of knowledge here...
 
Also by backing things up, what all is backed up? For example, does it back up my Rock Band 2 created characters? Or my LittleBigPlanet levels or Modnation Mods and Karts? What about any photos, music and videos I have on the PS3? Basically, what is BACKED UP with the BACKUP UTILITY?