Anyone else own it? With an afterburner installed, it is undoubtedly the best handheld on the market, surpassing even the GBA SP.

And to give this thread a bit of a theme as it were, I'll go ahead and list the games I own:

Mario Kart: Super Circuit - One of the best multiplayer games for the GBA
Super Mario Advance 4: SMB3 - It's SMB3 for the GBA, what more could you want?
Kirby: Nightmare in Dreamland
Rainbow Six: Rogue Spear - I am honestly suprised by how well this works on the GBA
Metroid Fusion - See SMA4 comment
Duke Nukem
Doom
Sonic Advance 2

Furthermore, I am in need of a good game that I can just load and play for short periods, namely a puzzle game would be ideal. Any suggestions?

Wario Ware my friend.  Wario Ware.  It almost beats out Tetris for that title.

In general:
GBA is teh omnibus.  (That's a good thing. )

I was thinking about getting an Afterburner kit, but for the combined cost of the kit and a soddering iron, I decided I was better off trading in my GBA for an SP.  (I was also somewhat apprehensive as I've never soddered before. )  The SP almost bests the GBA with an Afterburner installed, but its problem is the "crab claw" you get from playing on it.  To be honest, I recommend the Gameboy Player if you can afford it.  Sure it kills portability, but it is quite sweet to play on the big screen, especially with GBA games supporting rumbling features now.  (It's really the only way I play FFTa.  I also played through a majority of Super Mario Advance 4 that way.)

For those of you wanting a price break-down...

GB Player: 50 USD (I believe the GB Player is non-region specific.  I'll have to double-check.)
GBA w/ E-Reader: 50 USD (The GBA is non-region specific.  So too is the E-Reader I believe, but Europe isn't getting the E-Reader so most games there have the E-Reader support nixed.)
GBA SP: 100 USD (Region-free.)

Er... oh yeah.  For those that don't know, the GBA SP does not have a headphone jack.  You'll have to buy an adapter that'll convert the recharge port (pretty sure it's the recharge port,) into a head phone jack.  It's around 5 or 10 USD I think.  The one thing that is nice about the SP is that the speaker is centered rather than off to the side.  It also, in my opinion, sounds much sharper and clearer than the normal GBA.

Tetris. woot.

Yes it did.  It's pretty much a straight port of the PC version and not the SNES version.  That's good and that's bad in my opinion.  Good in the fact that nothing is censored and the dogs are actually dogs.  Bad in the fact that the SNES version was supposedly an amalgamation of the PC and the Mac version, (meaning it had the flame thrower and the bazooka as well as slightly updated graphics.)  I was also hoping for the developement team to throw in multi-player, but that was just wishful thinking.  I'd only get it if you're a big fan of Wolf-3D or can't run it on your PC because of its age.  

Er... well I don't actually own the game nor have I played it.  I searched around though, and the left and right shoulder buttons are dedicated for strafing left and strafing right.  A and B are used for firing and opening doors.  I'm not quite sure how you switch weapons, but I imagine it's either bound to the button that opens doors or maybe start or select.

I also found out something that may dissuade you from purchasing it.  It has no background music what-so-ever.  I'm not sure why they stripped that out.  The overall sound quality is also poor from what I have read.