Suggestions on how to get security camera video from a gate that's 800ft away

You could try HomePlug if you have an existing 120V run you can isolate, MOCA with coax, or you could use some LOS wireless solution.

You can add PoE extenders for longer distances.

http://www.veracityglobal.com

Fiber is likely cheaper, and more reliable in the long run (pun intended). When you're talking about making network connections across distances you also need to consider outside disruptions like lightning and other electrical faults. Using fiber pretty much eliminates that as a risk for your network equipment. Since it's just one camera you really don't need much bandwidth. I'm guessing even a 10 megabit fiber adapter would suffice, but you'll likely find 100mbit more commonly available. That and you don't introduce anything odd. It's just a network connection, not something that's trying to piggyback onto something else. Just be sure to pull a fiber that has double the capacity in the event something breaks. Don't just pull a single pair, pull a two-pair (four strands). That way if anything's wrong with a fiber you'll have two others already pulled.

http://www.veracityglobal.com/products/ethernet-and-poe-extension/longspan.aspx

Long range ethernet (800 meters) with 802.3at POE sources. There are a number of manufactures out there for these type of products :-)