I got the game not that long ago and am already in love with it. I'm not finished with the game yet but am already dreading the end of the experience. Thankfully DLC did come to the PS3 version and I'm debating whether to buy the Game of The Year Edition for the DLC (yes, I'm willing to buy another copy) or just download them individually over PSN.
 
I ask because I've heard people say that not all the DLC is worth playing, which if that is the case I'll just download the essential ones (like Broken Steel) over PSN and not the others. Also, I just want to know which purchase would provide a more stable, glitch-free experience?
 

I don't see why you would spend another $60 just to have the DLC. The only one you should really get is Broken Steel, and maybe Point Lookout because it's better than the others.

If you absolutely love the game just get them all, but if not just get Broken Steel and The Pitt.

It seems like Broken Steel and Point Lookout are the essentials from what I've seen.  Then again I bought the GOTY for PC so I can't complain that I have the others.  It seems like you could skip the Pitt and Mothership Zeta if you are tight on cash.  Operation Anchorage though I heard has some good loot but that is also a contender to be tossed if you are strapped for cash.
 
However I don't see where you could go wrong if you bought all of them either.

All of the packages have their perks. Anchorage awards you with what is, basically, the best armor in the game, for instance. And Mothership Zeta gives you access to some of the most devastating weapons in the Fallout Universe. 
 
In terms of sheer enjoyment, though, I'd have to say Broken Steel and Point Lookout, as has already been opined, are probably the two best pieces of content Fallout 3 has to offer.

Broken Steel for the level cap increase. All the other DLC packs were garbage.

Broken Steel and Point Lookout were my two favorites.  The Pitt was boring, but has the ammo press and some.... interesting new weapons.  Op Anchorage sucked and was only worth it if you glitched out the weapons.  I never bothered with Zeta with all the shitty things I heard about it.

I actually bought it a few days ago and am considering returning it for a copy of the GOTY edition so I can get all the DLC. I know some people say not all of them are equal in terms of quality, but I still think I'd get some fun out of them.

Go for all of them, some are better than others but they are all awesome!

Def. Broken steel. I could pass on the pitt, to be sure, and definitely the one that takes place in alaska you can pass on aswell