There's a little thing about "personal opinion of a new fan" vs "qualified answer from a seasoned watcher." In order to truly have an informed opinion of the best anime, あなた need:
*At least 10 years experience in watching anime.
*Watch regardless of target audience: shounen, shoujo, jousei, seinen, chldren.
*Leave personal taste behind: The best アニメ will never be one of your favorites. Your お気に入り is either going to be a genre starter that another アニメ did better, a harem series, hentai/yaoi/yuri, something terribly unoriginal where the basic plot has been done to death.
*Experience in critiquing: Being able to point out the merit of things あなた hate & point out the flaws of things あなた love.
Expand your horizons: Don't just watch series, watch stand-alone 映画 & OAVs. Don't just watch new shit, watch stuff from the 60s, 70s, 80s, & 90s.
Exquisite memory: If あなた have trouble remembering the names of the main characters in a 表示する you're watching right now & have to continuously look them up over & over, you're not the best person to ask. (I have a debilitating memory retention problem).
Experience: Ask yourself, with the thousands of アニメ available, have あなた even seen 100 different series yet?
Less is more: The best アニメ is likely not a series but a completely serious stand-alone animated movie based on a critically acclaimed novel.
Basically, even if あなた don't share his taste, アニメ critic "Bennet the Sage" is one of the few people who's answer I'd take seriously.
Well like likalaruku says, its pretty much based on personal opinion. I've seen alot of series though i cant remember every one, some just bits an pieces. i have watched OVA's, movies, all genres from G to X, an though i'm no critic または have seen em all, this is, like said, based on personal opinion, i think as far as story telling, Code Geass, is one of THE BEST アニメ i have watched. It has a great plot with interesting characters. i think it is a wonderful story methodically told, it'll keep あなた guessing an on the edge of your シート, 座席 till the very end. for me, its definitely Code Geass as THE best アニメ i have seen so far :)
Okay i have three anime's currently tugging for first place: FMA/ FMAB: this is totally a great one. I have so many fond memories of it and it has so many different things to like about it. Death Note: Will make あなた think and keep あなた on the edge of your シート, 座席 with it's murder mystery investigation. Clannad/ After story: So unique and takes the cliche high school romance idea and makes it something unforgettable. I finished this not to long 前 and am still amazed によって how good ti was.