Axton has quickly moved up my list of favorite characters in BL2, his turret action skill is quite good on its own, but with the right skills and weapons you can do the work of two players by yourself.
First the Survival Tree, I'm not a big fan of this.
Build here: http://talent.87bazillion.com/2/commando.php?41030000005500010000055050130151
You can see the relative offensive weakness of this build at about 4:45 in the video I throw a turret on each side of a basic loader, and I still have to kill it myself. I don't recommend the turret without the rocket pods. :) If you had 3 more points you could get the Scorched Earth rocket pods too. So with the 11 levels coming April 2, that's what I'd suggest first. If I did this over, I'd probably go with the rockets over the longbow just for the damage boost, but mag-lock without longbow is not very useful and Battlefront (extra damage when the turret is out for all your guns and grenades) is just so damn useful that I can't really recommend either version of this build unless you get the level cap DLC and get all 3 this build falls apart.
Now the Guerilla tree, the fun starts to pick up.
This is a good damage build with decent survivability. It allows the turret to slag, which is useful and will be even better in the upcoming third play through. The turret also has rocket pods and a shield. As far as Axton himself, he gets to carry 5 extra grenades and his shield will be recharging quickly most of the time. This is a good build that will only get better with the 11 new levels, allowing you to either add longbow and battlefront or get the twin Gemini turrets. Very versatile.
Finally we get to Gunpowder. NUKE!
This build is a great all around build as well, you still get the rocket pods from Guerilla and a good amount of defense, but you get a ton of DPS both from your nuke turret (basically an awesome, rechargeable grenade) and the use of the Battlefront skill. You'll note the Kerblaster assault rifle in the video shoots a projectile that explodes, drops a grenade and explodes again. This works with all the grenade damage boost skills too so this is my current favorite high DPS build. With 11 more skill points you can reach the slag turret too (double up, at the bottom of Guerilla tree) which will make this build very useful for the third play through. Also, nuking things is fun. :)