This is a tough one. I’ve seen a good amount of anime, and without a doubt there are more than 10 that are deserving to be on my top 10 list. That beings said, I’m going to base this list solely on my enjoyment factor and leave out silly things such as whether the show is actually good or not. I’m also doing this list in reverse order from top 10 lists because I can.
1) Code Geass – Lelouch vi Britannia commands you… to watch this show. For pure entertainment value, nothing comes close to Code Geass in my opinion. Is it realistic? No. Is is made of complete and pure awesomeness? Yes. The music is amazing and sets the mood perfectly. The animation is superb, and the voice actors are top notch. Especially Lelouch. And Charles (REROUUUUUUUCH!!). Did I mention that this series has my favorite ending of anything I have ever seen, anime or not? If you have yet to see this awesome series, do so immediately.
2) Rurouni Kenshin: Trust and Betrayal – My favorite of all animated films. If this movie stirs up no emotions in you, then you are incapable of feeling. Spectacular animation for when it was made, and a phenomenal soundtrack. If you want to watch something Rurouni Kenshin, then make it this movie. It’s actually a prequel to the primary series, so you don’t need to have watched or read any of it to make sense of this masterpiece.
3) Princess Mononoke – As cliché as it is, Miyazaki is definitely my favorite director of animated films. Princess Mononoke is his masterpiece. This work of art features beautiful animation, Joe Hisaishi providing an amazing soundtrack as always, and an incredible story. This is actually a great movie to show a friend who you may be trying to get into anime as this movie (as well as most Studio Ghibli films) is very Disney-esque.
4) The Melancholy of Haruhi Suzumiya – Why? The simple answer is that I’m not entirely sure. Something about this anime just drew me in from the start and out of all of the series that I’ve seen, this is definitely the one which I’ve seen the most. I can pick out any episode from this and it’s instant good mood for me. I have yet to show this to someone who disliked it, so give it a try for sure! Oh. Be wary of the second season though.
The Melancholy of Haruhi Suzumiya on AniDB
5) Fullmetal Alchemist: Brotherhood – This series holds the record for largest anime marathon which I’ve held. I started on it a few days before the final episode aired, assuming that I would have plenty of time to get through 63 episodes by then. Oh, was I wrong. In 2 days I had blown through 59 episodes. It would have been 63, but I decided to save the last 5 for back to back watching. It didn’t seem likely, but this outclasses the first Fullmetal Alchemist series in almost every way. Honestly, the only thing I can think of which I preferred in the first series was the music. If you’re looking for a shounen anime with great action and an even better storyline, look no further.
6) Ouran High School Host Club – In complete honesty, I don’t think I have ever laughed as much as I did while watching this series. This show is absolutely hysterical. Despite being the funniest show I have seen to date, it still manages to have some good drama! What more can you ask for? While it may seem like an awkward show to get into for us guys (due to its apparent girly nature), if you can get past the opening song and watch an episode or two you’ll be glad that you did.
Ouran High School Host Club on AniDB
7) Death Note – Another cliché pick. It would definitely be higher on my list if it wasn’t for the deterioration of quality in the second season of the show. This series definitely has one of the strongest starts of any show I’ve seen to date. It completely pulls you in from the first episode, and doesn’t let you go for a while. Death Note uses one of my favorite animation styles that I’ve had the pleasure of seeing as well as a phenomenal soundtrack to back up the even more extraordinary story.
8) Mushi-shi – If you ever need to just chillax and feel good about everything, this is the show for you. Mushi-shi is probably the most calming thing to ever occur in my life. I don’t know how many times I’ve gone to sleep with this series playing in the background. About 90% of the soundtrack itself is on my sleep playlist. This series does, however, function as more than a sleeping aid. It has a unique take on story telling which is done extraordinarily well as each episode tells a different story. Mushi-shi also features some of the most gorgeous animation I’ve seen. If you’re not so much into the hyperactive anime scene and want something mature and calming to watch, Mushi-shi is for you.
9) Welcome to the NHK – Welcome to the NHK is a spectacular mix of comedy, drama, and all out insanity. The animation may seem a little sub-standard at first, but it ends up fitting the anime perfectly. I definitely had many an LOL moment while watching this show. Welcome to the NHK also does a spectacular job of making it very easy to relate to at least one of the primary characters of the series. This is something that many anime have a problem with, and this itself can lead to one losing interest in the show. Welcome to the NHK also features a nice soundtrack (which is far more important than most people think in my opinion). I actually ended up working on the second ending theme on piano. Definitely give this series a shot!
10) Beck – Maybe it’s because I’m in a band/have a solo music project, but Beck really stood out to me. Yes, it has awkward Engrish right and left. Yes, the animation seems sub-par compared to other series which came out in the same time period. However, the story and music are just inspiring. Beck features an amazing soundtrack (as it should, seeing as it’s a show about a band), and a great cast of unique characters. If you’re into music at all (why wouldn’t you be?), then give this show a watch. You won’t be disappointed.
That’s it for now. This list, of course is subject to change at any moment. Give one (or all) of these a watch if you haven’t already!
Honorable mentions: Howl’s Moving Castle, Bakemonogatari, Baccano!, Elfen Lied, Original Fullmetal Alchemist
Animetem 
Code Geass is made of pure awesome. I only made it through the first season, though. I really need to start that up again.
You do indeed need to finish Code Geass :p