William Clinton's greatest act as president was to popularize the term wonk (technically know spelled backwards), which seems more acceptable than geek.
Either way, my (self) definition is as follows, which unfortunately includes myself:
A person who is so heavily involved in a field that they at least occasionally lose the ability to communicate their knowledge to non technical people. Every field, from the sciences to art history, has technical jargon and a rich history of meaning that only a geek can appreciate.
The result is that when a non-geek asks a geek a question, the geek will often explain way more than the non-geek is interested in (or capable of understanding). Geeks understand something in DEPTH, usually in excruciating detail, as well as the high-level view.
What makes them geeks instead of scholars (in the eyes of non-geeks) is their inability to reach the non-geek at their level of understanding. So, many teachers are inadverdant geeks, as are some archaeologists and art historians, and some sports enthusiasts.
The geek phrase used to be the non-geeks way of leveling the playing field, by overcoming a feeling of not knowing with a feeling of being socially superior. Thank God that is changing, and geeks are finally garnering some respect.
The short form of my definition of geek: someone who knows so much about a topic that they sometimes have difficulty communicating with those who do not know as much on the topic.
With our advances in technology, eventually, we will be a planet full of geeks, and will have to grok to be able to talk at all.