I have a game room over my garage. I want to put a wet bar on the far end of it. This is about a 35 foot run from my laundry room where I can tie into existing supply and drains. Do I need a vent for this?

Yes you will need a vent for this sink.
If this is going to be a island sink you could use an Air Admitance Valve for the vent. Here is a post that shows a loop vent in case you needed one.

https://www.askmehelpdesk.com/members/stew_1962.html

Yep, you definitely need a vent for the bar sink. As letmetellu said, you may be able to use an aav(depending on what code you fall under), but I suggest running a vent up and out through the roof.

Yes you will need a vent for this sink.
If this is going to be a island sink you could use an Air Admitance Valve for the vent. Here is a post that shows a loop vent in case you needed one.

https://www.askmehelpdesk.com/members/stew_1962.html

Hi all:

Letmetellu's links aren't working so I thought I'd pop in and put up the diagram of the island vent system he was talking about. Although quite involved, this venting system is required in most areas.

You can also install an air admittance valve (AAV... see image) in place of the island vent, but it may not be considered legal in your area... up to you. Install the AAV so it is a minimum of 4" above the trap... it can go higher as well.

MARK

Thanks all, you've been a big help.