So recently I was asked to do jazz (piano player) for our band. I started looking at music for jazz and I see a lot of the time, there are chords. But some of these chords require jumping around or weird fingerings. Can I use the sustain pedal for the chords so I can have the next prepared or is this nontraditional and wrong.
The sustain pedal is there for just that purpose - to hold notes on while fingers do something else. If a piece can be played smoothly without, then there's little or no need to pedal. It the piece has stabs, there's definitely no pedal needed. So, it depends on the piece. Jazz, classical, folk, it doesn't matter what style. Use it if you feel the need - it's part of playing the piano.
The sustain (damper) pedal actually does more than merely sustain, but that's not an issue here, or in playing jazz specifically.
In a jazz band, whatever it says on the music you're given, the main rule is PLAY LESS! The piano book may well include the bass line, but if there's a bass player, leave it to him. Likewise, if there's a guitarist taking the 'rhythm guitar' role, leave that to him. Sometimes it will be your turn for the melody, but not ALL the time! I don't think you'll find much need for the sustain pedal.
I play piano sometimes with a banjo/clarinet duo. The banjo player is used to providing the rhythmic drive with constant strumming. What's missing is the bass line. So, in that band, that's MY job. Often my only job. That's fine.
There are a lot of good answers here, and Tim and Laurence have some great rules of thumb (try to play smoothly without pedal, only play primarily what the other instruments aren't playing, etc.).
I wanted to add that when a pianist plays stride (solo), the left hand jumps around a lot, and it sounds choppy. When I listen to just the left hand, it doesn't sound very good to me. But when the right hand is playing along too, it can sound great because this choppiness is covered up by the right hand. This is especially true at faster tempos. If Bram were to use pedal on that song, it would sound really muddy.
So those are some "guidelines" for solo piano when playing stride. But something similar can happen in a band: the other instruments can have a similar effect of smoothing out a choppy-sounding piano part. So before you add in the pedal, you might want to wait to see how it sounds with the band.
That said, it does all depend on context, as Tim states. There is a technique where you pedal before each bass note, but this probably won't sound good at higher tempos or when playing in a band. When playing a ballad, pedal can make a lot of sense. In that last link (of Dan Nimmer), you'll hear the technique again of pedaling before the bass note.
All of these answers are great, but I just want to add somethings I know from experience.
I used to play in a combo (I know, not the same thing, but the concepts apply) with this pianist who used to be very sustain pedal heavy. The problem with that was, when solos would pick up and such, everything would sound terrible.
Here's there reason: when you press the sustain pedal, you lift off some padding from each string in the piano. So now, when any sound is made near the piano, the string in the piano vibrates.
This could mean that a horn's notes are sustained behind them as they are soloing. In a big band setting where you've got a bunch of instruments playing a bunch of different notes, this can lead to really muddy situations where the horns have switched notes, but the piano is still ringing them.
That's not to say the pedal is not to be used -- just keep this in mind and listen out for this.