A personal that is addicted to being on the internet. They typically are either on a social network or online game more time during the day than doing anything else.
A web geek can also be considered as someone who uses the internet to do most things, such as, research, buying clothes, food, electronics, cars, houses, and date.
Another example of a web geek is someone who knows everything there is to know about the internet, such as, how it started, it's history, it's protocols, and the best websites to visit.
"He is always on the internet."
"Yeah, I never see him doing anything else."
'He's such a web geek."