BEST ANIME EVER
Well the best of all time IMHO is Full Metal Alchemist: Brotherhood.
The original FMA was awesome and had one of the most disturbing scenes in anime or any movie I have ever seen. They spent an entire story arc, maybe 3 episodes I can't recall, telling the story of this alchemist and his young daughter and their dog and I won't ruin anymore of it in case anyone hasn't seen it. It definitely had an effect on me.
They really improved FMA and the story arc with Brotherhood imo. Watch both, and then tell me which one flows better :P
Second best IMO is definitely Bleach. Its a very diverse cast, with very real and relateable characters and EPIC battles. I love it. Ichigo Kurasaki is a much more relateable character for me than even Edward Elric in FMA. I gravatated more towards Roy Mustang in FMA anyways.
So yes, did I name two of the most common anime, probably. Is it because those are the only ones I have ever seen? HELL NO. Sometimes things are common and popular because they are GOOD. Now I am not die hard and there are probably more anime that I haven't seen than have seen, but I will standby the storylines, character depth and EMOTIONAL involvement the viewer feels in the characters storylines. Maybe it is just me, but both storylines really sucked me in and I felt myself reaching the highs and the lows with the characters in both stories.