K-ON is awesome! There is an OAV too, gonna watch it soon ^^
On topic... Hard to make a full list when we don't know what genre you like and also if we have to stick to the "13 eps" thing xD. Anyways, some animes :
- Angels Beats
: Amazing anime with some action, drama, music... It's like K-ON with a "band" and some music during the episodes. High chance you'll cry at the end...
(like woeaih4 mentioned) : One of the funniest anime ever i think ^^ season 1 has 8 eps, the second season 13.
- Highschool of the Dead
: Students and zombie invasion, do i need to say more? (fan service too ^^).
- Black Lagoon
: Action, violence, etc. First season is 12 eps then if you like it there is a second season with 12 eps too and even a "third" (well so to speak) with 5 eps.
- Ergo Proxy
: Science-fiction, drama, cyberpunk, adventure, etc. Really awesome.
- Elfen Lied
: Drama, gore, violent. Check it out if you like this style. It's non violence non-stop/action but some scenes can be difficult to watch.
: drama, romance, it's cute if you want to see something else and not only action animes ^^
- Lain (Serial Experiment Lain)
: An old anime and really... weird but awesome IMO. It's about computers, mystery, drama, psychological, etc nothing to laugh here ^^
- Kimi Ga Nozomu Eien
: Romance, tragedy, drama... yeah you gonna cry.
- The Melancholy of Haruhi Suzumiya
: Comedy, school; science-fiction. First season is 12 eps, there is a second one but haven't see it yet. It's a great anime.
But you should not focus only on such series, there are awesome animes that have like 24 episodes or some have several seasons
Check out the database from http://www.animenewsnetwork.com
to read more about each anime to see if you like the story/genre!
Hope you find some animes you like