Here's something interesting Wikipedia had to say:
The Velvet Underground was an American rock band first active from 1965 to 1970 (and 1970 to 1973 in a different incarnation). Its best-known members were Lou Reed and John Cale. Although never commercially successful while together, the Velvet Underground are often cited by critics as one of the most important and influential groups of their era. A famous remark, often attributed to British musician Brian Eno, is that while only a few thousand people bought the first Velvet Underground record upon its release, almost every single one of them was inspired to start a band. Their sound influenced many later musicians in many genres, including experimental, post-punk, new wave, and gothic rock.
What I want to know is WHICH bands did they influence? Anyone know?