AiAi recommends:
Anime that has cute chicksLova Hina - Comedy/Romance/Shounen. Features 6 girls who live in a all female dorm, and Keitaro, a dorky male as their manager and looks after the place. It's a funny silly anime, that can get downright stupid at times

. You can get the 24 ep. boxset for $101.39 at FBO.com.au.
Tenchi Muyo! OVA - Science Fiction/Comedy/Romantic Comedy. Not only is it regarded as the king of harem anime, but one of the best and most original anime of all time! About Tenchi Masaki, a boy who hasn't had any luck with women. To quote: "Soon, a whole bunch of girls are after him -- a space pirate, two alien princesses, a space detective... just about every female who gets to know him, wants him."

I bet you are tired of me going on and on about the show, but it is that good. Trust me. What makes the show really good is the quality of each episode. There is no filler episode and plenty happen in each of them and there is a lot of character development. You will learn a lot about the characters and develop feelings for them. Also, the humor is really good, especially the timing of the jokes. Plus, there is plenty of catfights!

For more info, read this
review. Love Hina can get silly at times, but Tenchi Muyo! can get even more sillier and you will be amazed at how far the writers where willing to go! You can get the 13.5 ep. collection for $74.64 at FBO.com.au.
ActionCowboy Bebop - Science Fiction/Comedy/Adventure/Drama. There's nothing original about Cowboy Bebop. But the way it is done; the style, the music, everything is done really well. About space cowboys (bounty hunters) who will do anything for cold hard cash! You can get the 26 ep. boxset for $112.20 or $125.86 (*is confused*) at FBO.com.au.
Naruto - Adventure/Comedy/Shounen. If you are willing to give your boardband connection a good workout and willing to play catch up (at time of writing, the show is up to ep. 77/78), Naruto has plenty of action, ninja style. The pacing can be slow at times, but some of the fights are awesome.
There are way more action anime, but I've only listed the I found really good. People say Trigun is great, but I found it to be only "good".