Do I need to install dry wall in my basement?
What drywall will give you includes:


Insulation. Concrete is not a good insulator, so drywall will help here, and as @ChrisF points out in the comment, you can add insulation behind drywall for some extra.
Soundproofing. A bit of soundproofing, anyway
Somewhere to run cables behind, so they aren't exposed. Depening on where you are this may be a requirement
Simplified shelf mounting etc.
Much easier to cover/paint - you can use normal paints on drywall