I'm a mecha anime fan. I watch anime to unwind so I'm not big on series with massive complicated plots (Code Geass and Gundam are as complex as I usually go). With that in mind, here is what I would recommend if you are looking for fun, action filled anime:
Code Geass - all round fun to watch, it goes down a little toward the end but the finale makes up for it. Good political mecha anime with a main character who outsmarts his opponents in ever more impressive ways. Some really clever moments and loads of great plot twists.
Gundam 00 - it's a new take on Gundam, very cool. Politics and mecha blend again, but in the early episodes more episodic and focused on the core cast. The Gundams are powerful but never too powerful - but the end of the series, the other side outclasses them. Season 2 is still airing, it is the best Gundam has been in a long time. All round good show and worth checking out.
Gurren Lagann - Gurren Lagann is a slick, high action anime which invites you to kick reason right out the door. It's fun mecha action with "burning courage" to the utmost maximum, slick battle sequences and all-round retro mecha anime fun. The creators must have been fans of Mazinger and Getter, because the love shows. The series brings out all the fun of mecha anime that series like Evangelion killed off by getting too focused on the characters. It's ultimately like Gainax's other anime, Gunbuster, in the level of action and sheer fun.
Gunbuster - Gainax's original anime, it is another good short series. Some really epic battle sequences, and classic super robot action in the later episodes. The early ones juxtapose againstit quite well developing Noriko from an unsure schoolgirl into the heroic pilot of mankind's strongest weapon.
Gaiking: Legend of the Daiku Maryu - This one I've got a special spot for. It's a remake of a 70's series but it basically just took a few key elements. What made it good was an emphasis on action, without stock footage. Every attack and technique was thought out in battle, and there are some clever fight sequences. Plus everything is slick, and flows well, with some truly clever bad guys and one of the best mid-series moments ever.
Also, the crazy episode with the purple hippos.
Gaogaigar / Gaogaigar FINAL - I'm a huge fan of this series. It's more super robot action which does not need you to think about things - it's pure action and fun, with a good dose of guts and "courageous hearts win any battle" on the part of the heroes. It's over the top, it's retro, and above all else, it is fun to watch.
I'd also recommend checking out Koutetsushin Jeeg, another modern update of a classic, Getter Robo: Armageddon, New Getter Robo and Mazinkaiser (especially the movie where he fights Daishogun and the other Great Mazinger villains).