In your Starcraft directory, open BrooDat.mpq and StarDat.mpq with MPQ Editor 1.2 (
http://www.angelfire.com/sc/mpq/). These MPQ archives contain the units voices in .wav format that you hear in the game when selecting and commanding units.
For the in-game conversations, storyline voices, etc... get both your Starcraft CD and your Broodwar CD out. On the CD there should be a large file (~500MB) - on the Broodwar CD it is called INSTALL.EXE (545MB). Copy those 2 large files to your harddrive so that you can access it quickly using the editor. Yes, these files use the .EXE file extension but they are infact archives. When opening an archive using the MPQ Editor 1.2, you will notice it accepts .mpq, .exe, & .snp.
Once you have the archive opened, you will have a list of all the files in it. You can double click them to temporarily extract and run them, for example, if it is a wav file, double clicking it will play it in your music player.
Do have the game CD(s) or do you want someone to extract them for you?