You n00b
You would see them everywhere - they are arguably the most popular series out there at the moment - although in my honest opinion I think it's time Naruto and Bleach get retired, since both those series are getting on my nerves - and probably stopping a lot of people from getting into anime - because anime get's pigeon-holed into the "oh, its a lot of fighting and power-ups etc" trap.
The series BlaZing mentioned are all pretty good ones - Death Note is actually very far away from childish, and worth a watch. Other than that, suggestions can vary greatly depending on what your preferred genre would be - action, comedy, romance, sci-fi, drama, suspense etc etc.
There's almost no limit to the number of series available.






