Only manga so no anime, right? In that case, here's my list: (This list isn't in order of my favorites)
1.
Fairy Tail- It's a got a great plot that'll just hook you in.

And the characters are very likable as well. ^^ Perfect for anyone that likes some adventure, comedy, magic, and the occasional sad parts.

I found the art a little iffy at the beginning, but then later the mangaka improves A LOT. (And yes, A LOT)
2.
Dengeki Daisy- A great shoujo manga that doesn't follow the same boring typical plot. I think the best part about this manga are the characters (Well, the story is really good too). After reading many shoujo mangas, I came to the conclusion that there are three main types of boys: The really popular and social dude that many girls like, the really smart and aloof and perfect dude that nobody can really talk to, and the abusive dude that takes advantage of the heroine (usually in a sexual way), who somehow falls in love with him. >.> And then for the girls, there are mainly these types: The super clumsy, idiotic girl that needs help all the time, the super strong and manly girl who is trying to hide that strong side of hers, and plain jane. But the two main characters in Dengeki Daisy aren't any of those, and instead of personalities that you can see a real person having. (Whoops, I typed a lot more than I expected to). Anyways, this manga is great for people that enjoy a sweet little love story that has a great side story to go with it. This manga also has some sad parts.

3.
Ao Haru Ride- Another shoujo manga.

The characters are a little typical compared to Dengeki Daisy, but they're still really likable.

What I love about this manga is HOW CUTE AND ADORABLE IT IS!!!!! I mean, I don't think the mangaka is trying to do that, but I can't help but think how the interactions of the main two are so cute that I end up rolling on the floor while squealing like a pig (Yes, I'm weird). This manga also has a little bit of sadness in it.

(If you haven't noticed it already, I kinda have a thing for sad mangas/animes

)
Okay, I'm typing a little too much so I'll just list the rest with a little bit of info:
Durarara! Very interesting story that hooked me in right away.
Love So Life Very cute shoujo story, though the development is a little slow
Hapi Mari Fun read, though it's for an older audience.
Deep Love Series Really sad a touching; also for an older audience
Kimi Ni Todoke I really like the art, the the story is realistic, but it's a little too slow for me.
Fruits Basket A sweet and cute story.
Hiyokoi Cute story, but sometimes the main girl annoys me.
Liar Game Very interesting and makes you use your brain. Also makes you wonder how the author came up with it. (Since it requires quite a lot of brain power)
Sora Log Sweet manga, though the art isn't the best.
Mars I actually don't really like the art in this manga, but the story is really good. A little disturbing though.
Flower of Evil A really disturbing manga about these two twins that are in love with each other. But it's also a really interesting story.
Vampire Game An interesting, fun, and funny manga. the art isn't the best, but it's not bad either.
Wish The very first manga I read. Sweet story, though the art is just okay.
Velvet Kiss Really great art and great story, but is definitely meant for an older audience.
Okay, I have a ton more, but I'm gonna stop right there. XD