I've been saying some less than positive things about WoW's automated dungeon finder of late, so it seems only fair to give equal time to one area where I've been getting a lot of benefit from the system - groups for leveling dungeons.
The logistics of LFG
Historically, I've always simply skipped over leveling dungeons. The nebulous (generally lengthy) amount of time it would take to find a group before you even start the actual dungeon run was too much unpredictability for my schedule. On top of that, dungeons often represent the culmination of the storylines in a given zone, meaning that you will be out of stuff to do in the neighborhood by the time you have all the relevant quests. Though WoW did have dungeon summoning stones, at least two party members needed to travel to the stones (often as many as four of your party members may presume that someone else will summon them), and the greatest concentration of players looking for groups for a given area are often located in that zone's local chat.
The dungeon finder blows all of these concerns out of the water. As a DPS, you're going to be looking for something like 15-30 minutes, and you can do whatever you want with that time, as you will be teleported to the dungeon automatically when a group is assembled. As a result, my Warrior has been doing every dungeon in Northrend as soon as the relevant quests become available, earning significant gear upgrades in the process. I've even queued up for random dungeons when I feel like I could use a change of pace from solo questing - my warrior has already banked a handful of emblems and stone keeper shards from these efforts.
A different take on the public quest
When Warhammer Online was getting ready to launch, I was actually very excited about the concept of public quests. The idea, as Mythic described it, was for players to get to enjoy high quality group content without having to deal with group logistics. Unfortunately, because these quests were non-instanced events located in the outside world, population worked against them. You might show up at a PQ and discover that there weren't enough players there to complete it, or you might find that too many had shown up, making the content trivial. Worst of all, you had to travel to the quest areas on foot, and could arrive to find that the party was over.
The way that the random dungeon finder has worked out in WoW is very similar to the end goal of the Public Quest - but with much of the random chance and logistic inconvenience taken out. Your group will have the right number of people and correct balance of classes for the content (though they may or may not be overgeared). You do not need to worry about travel, or even knowing where it is that you should be going (though this can be a problem when players die and don't know how to get back to the instance).
There may be no removing the social downsides of working with strangers in group content. I also maintain that the system should do a better job of maintaining difficulty by using appropriately geared players when possible - one random Old Kingdom group, a level 74 dungeon, ended up with a level 80 tank for some reason. When it comes to the actual goal of making group content accessible to players as they level, though, this system is a huge success.