Are there any Rocket Propelled Grenades in the Fallout series? If so, are they worth using?

(I note that the original Wasteland had them, but they were worth so much that it was probably better to sell them than to actually use them.)

Yeah, same thing. Bazookas. Effective but too heavy and expensive to be really useful.

They are worth, they cause tons of damage, but it's probably a good idea to spend points in small gun skill in the early game, if you don't want too much difficulty in your way to the first towns. Or steal the Advanced Power Armor, if you don't want to waste skill points in another combat skill.

There are a lot of rockets at Sierra Army Depot.
But you'll need a good weapon to get access to the facility, like Gauss rifle, Sniper rifle (there's one near a corpse, search for a big hole in the fence, in Sierra). If your small gun skill is awful, use an NPC to help you, give it to Cassidy or Vic.
I recommend having a high lockpick skill. It will make your life easier. Not only in this place, there are a lot of locked rooms in the game.

Theoretically you can have unlimited rockets, if you have a good party, or top quality gear and weapon.
Hunt remnants of Master's army, Broken Hill Caravans*, and if I remember well, rarely Enclave patrols have a soldier holding a rocket launcher.
San Fran shops get more ammo after some time has passed, but I'm not 100% sure if it's forever.
You can have infinite energy weapons ammo, for free, with T-Ray in New Reno (I can tell you how, if you don't mind spoilers).

Unlike Throwing skill, which is garbage, you can make a good character with Big guns skill.
If it's your first time playing, definitely invest points in another combat skill - Small guns.
Small guns for early game (even in mid/late game they're great) and Big guns for mid/late game.
Good luck.

* I don't think it will affect your reputation with the town.

I was talking about Fallout 2.
In Fo3/New Vegas ammo has no weight, even missiles and nukes, so that makes your life much easier, you don't need to ask your companions to carry them.
Both New Vegas and Fallout 3 have unique weapons, so you can find unique variants of missile launcher, which are more destructive than the normal weapons. Miss Launcher (Fo3) and Annabelle (NV).

Go here to see where you can find the weapons, and ammo for them:
http://fallout.wikia.com/wiki/Fallout_Wiki

If you play in Hardcore mode, ammo will have weight.