This one is a rather popular anime. You can read the description for what it's about. Angel Beats is nice because it's fairly simple with good animation and is pretty versatile.

If you want to watch one of the best horror animes there is, watch Another. No, not another anime besides this one, the anime titled Another. It's short but the pacing is  good and while horror is not a very strong genre in anime, this is a strong anime.

Assasination Classroom has some good comedy and action. If you don't care for the typical comedy than you might prefer this to a lot of the other comedy titles. It also has a feel good atmoshphere and a simple story.

This anime is a lot more serious and dark than a lot of other animes on this list, but it might also be the most exciting. It has good pacing and interesting characters. The story isn't too complicated and there is a lot of good action sceenes. I will warn you though, if you don't like blood and gore, you might want to skip this one.

Another popular anime with a fairly easy to grasp concept, interesting characters, and good action is Darker than Black. It's on the serious side. 

Fruits Basket is a simple, fun, innocent comedy that is also quite popular. The main character is a bit of an air head though.

This was among my first animes and I still love it. Some people might suggest the Fullmetal Alchemist Brotherhood series which follows the manga more closely and was made after this one, however, I think this one is a whole lot better. It's long, but it has a good mix of comedy, drama, action, and some very lovable characters.

This was either my first or second real anime (not including yugioh and pokemon because those barely qualify). It's pretty long but it was the anime that really got me hooked to anime. The characters are enjoyable and theres a bit of everything in this one. 

The ending to Inuyasha.

This is one of my all time favorites. It's a survival game type anime. It is a little crazy so I wouldn't reccomend it as your very first anime. Watch a few others before you jump on this rollercoaster. The English title is Future Diary.

SEXY BUTLER. That's really all you need to know. Actually, it's a darker comedy set in old England. It has some super lovable characters including the sexy butler, but the story is pretty easy to follow and it's pretty popular. It's also known in English as Black Butler

This has a good amount of comedy, although, if your like me, the first episode might make you wonder if you should keep watching. Fishes swimming by peoples heads and a glass of water....under the ocean, it seems a bit silly, but it's a nice heartwarming drama.

Another one of my first animes was this. It's a simple generic anime with some great sword fights in historical japan around the Meji era. 

The end of Rurouni Kenshin.

This takes place before the tv series but you can watch it after.

This is a fun episodic comedy with some gender bender and school themes. I'm not even big on comedy shows but this one is a must watch and it's great for beginners.

Parasyte is a great anime, although more serious and it has some blood and gore, but if you don't mind that, you will probably like it.

This was another one of my early animes, although I can't say it was a favorite. The story is less simple than most of the others on this list and it has a different feel to it. It uses giant robots to fight in the future. Still, I think it's a decent one for beginners.

Personally, I HATE this anime and think it's crap, but a lot of anime newbies love it for whatever reason so I put it one this list. I reccomend it but only because it seemed to be a big hit among people who never watched a real anime before, not because I think it's worth anything.

This was also among my first animes. Again, this story is a bit less simple and the characters are slightly more vague at times, but when I was new to anime, I absolutely loved it. I still like it now, but I just have a lot of animes I like better now.

Again, this was one of my firsts. The ending was a bit confusing the first time I watched it and I can't really say it made a whole lot more sense when I watched it years later however, I still love it. If you love wolves, you need to try this one out. There isn't much action or comedy though, and if you do love wolves, it's actually sad towards the end, but I reccomend watching it.