might be a stupid question.... but do they?

or will that damage the pedal somehow?

for example, if i have a boss ME-something that i use for a guitar, can i also use some of those effects with a bass guitar?

and before you ask, no im not planing to play my bass through a guitar amp as well.

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Some do better than others. Depends on the effect and the signal they are designed to work with.
fine for playing live, but they don't act very well as DI boxes if you wanna record your bass unfortunately
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It depends on the pedal. Delay, reverb, phaser and flangers are perfectly fine.
Simple distortions and fuzzes might work, some better than others. The more complex ones generally have an EQ section which is tuned to guitar-specific frequencies, so it might sound a bit odd for bass. However, if it just has a tone control, it should be fine.

I'm not sure about stuff like wahs and envelope filters. Those are also adjusted to a specific frequency range, so while they will work, they won't sound great.

You won't break anything by playing through it. It might just not sound as good.
A lot of pedals aren't meant for the frequency range of bass, therefore might suck out your low end a lot.

A Boss multi-effect pedal might work decent. You might be able to adjust the settings a bit to get more low end response. The overdrives and distortions might not sound great, but you might be able to get some good tremolo or delay sounds and stuff like that.
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Of course they do, and bass distortion pedals work with guitars much better than they do with basses.
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Asking the Pit to play this is kinda like asking the guy who makes suggestive gay jokes if he wants to have sex with a man.
The only thing you can damage using a bass in guitar gear is the speaker, as guitar speakers are not made to handle those low frequencies.