As anks329 said, the approval delay does vary quite a bit. My account was approved in minutes, but a friend I referred had to wait a few days for approval.
I believe DreamHost has an automated fraud detection system that tags some applications for manual approval. Exactly what factors trigger this process is unknown (deliberately so).
Save $50 on DreamHost hosting using promo code "SAVEFIFTY" ( DreamHost Promo Code )