If I were to make a mod that replaced the music for in-game, such as protoss1, protoss2, terran1, ect., would that cause other people to crash/drop over battle.net? Would be nice if I could use my own music during games instead of lagging with media player.

I don't think so.

I think that starcraft's engine just picks a random song (or whatever it does to choose) but doesn't necessarily have to be the same for all players in a game.
Also, this sounds like a GREAT idea, though, you'll have fat wav files as an outcost.

Yes! It works! You can change the music in the mpq and it doesn't affect anyone but you online - no crashes or drops!(Can't believe it worked. I accomplished something big in the modding section. )

I, personally, like making my protoss units look badass in melee via grps.

Just got an idea, If you're only putting music, you can try thundergraft to see how it works for you.

It'll allow you to play mp3 music, so yo save the whole wav conversion deal.
http://www.campaigncreations.org/forum/index.php?topic=1980.0

I was modder 2 or more years ago, and yes: there is a way to change music.
There's one thing you need: WinMPQ (sorry, I didn't find a link but if I find it, I will update this post)
First, you need to insert your StarCraft CD and copy INSTALL.MPQ, and place it in your StarCraft folder. When that's done, rename it into Broodwar.mpq
Second, open Broodwar.mpq with WinMPQ and look for music\terran 1~3 and protoss, zerg etc. according to what you need.
And that's it! if you want to change the soundtracks just extract old .wav files and insert new ones, but they must be .wav format.

Uh, or just use MPQDraft to run the mod? Much safer.