Hello, just started to play the game and I'm enjoying it so far, but the main reason I want to play the game is to do dungeons and other group activites such as killing hard mode named guys or world bosses. I was just wondering, how often do people do dungeons while leveling and are there a lot of opportunities to form a group and go kill big baddies in the world?

Also, if the game doesn't manage to fit what I'm looking for, is there any other game you guys would suggest?

The game is 3,5 years old and there are plenty of dungeons and people who run them

here is a list

http://aoc.wikia.com/wiki/Portal:Dungeons

Well...plenty of dungeons and other group activities in the game. However, it is a chore to find people to do them.

My opinion, your best bet is to join a good guild that fits your playstyle and group with them for dungeons. PUGs can be good and bad, but if you get into a guild you'll find people to do stuff with more than spamming global or LFG channels for a group. Some people have those channels off because of the constant crap that goes on in global.

Then again you might find your guild through a PUG. I found one that way awhile back when AoC first came out and it worked out really well for me until they left for Rift. 

Check the main forums for your server and the guild sections and send a tell to someone. Sometimes they advertise in global chat as well.

Goodluck! AoC dungeons are a lot of fun. Black Castle, and Sanctum are really good when you experience them for the first time. Same with Amp and seeing the Frost Giant God, now that is amazing to see.