I'm looking to purchase a handheld recorder under $1000. It needs to be able to pick up guitar, bass, and drums. Basically, I want to record my band's jam sessions, but i also want to be able to take it different places (outdoor acoustic, etc.).

Are there any out there?
Well you can check out the boss micro BR and maybe a dynamic mic for acoustic stuff, wont be great and u wont get much by way of a great drum recording out of it tho, worth a look all the same.
Fender Deluxe Strat HSS
Fender Standard Strat
Fender Highway 1 Tele
Epiphone Les Paul Standard
Orange Rocker 30 Combo
Seymour Duncan Twin Tube Mayhem
Roland Microcube
Boss Micro BR
Korg Pitchblack
EHX Holy Grail
Hohner 3/4 Classical
Very difficult question to answer without more specifics - how many tracks, on-board CD burner, effects - what is it you want exactly?

A very good cheap option is this;


I bought one last year and the quality is great.

However, I have this in my studio;


Which is another animal entirely.
I'd take the Zoom. I can't really see the point of a palm-sized 4-track recorder like the MicroBR, especially as I don't think it has phantom power. Get the Zoom H4 and perhaps a pair of good quality condenser mics so you can cover your jam sessions as widely as possible in stereo.
So the Zoom H4 has two mics built in, right? And can you then plug other mics into it?

edit- If you can plug mics into it, does it only record through the external mics, or the built in mics and the external ones?
+1 for the Zoom. Forget about Boss...... junk company. We use the Zoom to record practices and jams. Has 4 corner mic pick up and once you convert the recording file to WAV and burn it out to disk you get a really good sound quality. Plus it's only $250 or so.
96 Gibson Les Paul Goldtop
95 Strat w/ Lindy Fralins
Ibanez JS1000
Orange AD30HTC
Vox AC30
Blue Alnico Cab
Budda Wah
Barber Tone Press
Keeley NOVA Wah
Pederson Strobo
Keeley TS-808
HBE Chorus
T-Rex Delay
Red Witch Moon Phase