Shounen(Action and epicness but simple):
1-Bleach
2-One Piece(if you want to watch more than 300 episodes but it's good)
3-Naruto(I know people hate it because of the narutards but it's a really good anime.
4-Dragonball(the original), I don't know if it fits the shounen category but DB is better than DBZ, of course once you watched DB you'll want to see DBZ.
5- History`s Strongest Disciple Kenichi (I hope they will do a second season of it.)
Random/Slice of Life
1- Lucky Star (watch it or you'll regret it...)
2- Minami-ke (It's pretty new but awesome, a new version of the show just sarted I hope it's as good, but I don't like the characters new look)
3-Azumanga Daioh (It's pretty random and cute, it's funny too)
4-Genshiken 1&2 (Slice of life show about a group of otakus, each with a "specialisation")
Bleh I have trouble finding categories for all the animes I watched so that's it for now. I also recommend Death Note, Juuousei, Great Teacher Onizuka(With Shonan Junai Gumi, it's prequel), Welcome to the NHK and Excel Saga.
What I recommend you to do is take the title of the anime you might be interrested in and then search it on anidb.net so you will have a description of it and info like the number of episodes, groups that subs/subbed it, it'll be easier to find them after. Most of the time you can even click on the Group name and then you have it's website and download it from there. I started watching anime like you, asking GBAtemp, and now I downloaded so much stuff I don't even have the time to watch it all, haha.