You Should Try...

The LFG dungeon finder system if you're leveling a toon. The reason? You learn to play in a group, and as a result, gain some mastery of how to play your class and role in the group. I was leveling my hunter before the LFG tool came out, and made it to 80, with very few group runs. As a result, by the time I started running instances, my dps was very low (vendor arrows and bullets, not using much shot rotation: see too much auto-shot), etc. My paladin on the other hand, I've been running instances as often as I can. As a result, I've gotten a feel of what attack order I should do as a ret pally to gain most damage, and have found myself in a healing role more than once when healers had lagging issues, etc. That will only help me when the pally reaches end game content.

While I enjoy playing solo, (don't like some PUG drama I've experienced), running randoms can be a good thing. Not only do you learn how to play your class, sometimes you may find yourself in a group with some excellent players. Take my pally run in Zul'Furakk. It started shaky. One of the players (not a tank), was pulling mobs, and kept getting killed. The healer (who wasn't playing her role too well), let out some kind words for the group, and left the party. Well, we got another healer and DPS player, and cleared it out easily. We chatted with each other along the way, and complimented each other for how well the ran went.

In the end, you'll get a mixed bag of groups. You'll find abrasive idiots, players who aren't trying, etc. On the other hand, you'll find players who are really good at playing their class/role, and are willing to give advice if there's problems (see my hunter DPS) instead of just bashing you for it. Besides, the chances you'll see these players again are slim. If all you do is quest, try putting yourself in que for a random. It's an easy way to gain experience, learn your class and spec, and how to deal with group dynamics.