Officially... no. There is no way to just get upgraded for nothing at all outside of dumb luck (and being nice to your GA).

My general strategy goes something like this, and only works if you have the time to be bumped. If you absolutely need to be on the plane, I don't recommend this. I've had some luck with this (2 bumps with upgrades to F and one upgrade to F for no reason), so you might want to try it.

When you get to the gate, look around. If there are a lot of people and the gate agent looks a little frazzled, walk up to the counter and as nicely as possible say, "Hi. It looks pretty busy tonight, if you need a volunteer to be bumped let me know." Don't wait for them to call for volunteers. Volunteer immediately if there is even a whiff that someone is going to get bumped.

Odds are the GA will say, "I don't think we'll need you tonight/today, but I'll let you know." If you see them shuffling boarding passes behind the counter, you're going to be in. Again, don't bluff about this. If they call your bluff and you refuse to be bumped, you get nothing except a pissed off GA. After they tell you that they probably aren't going to need you tell them, again as nicely and as helpful as possible, "No problem. Just let me know if you need a seat and I'll be happy to help."

Then, go away and formulate your plan (you can do this before hand too). Look at the departure screen and check to see what the next flight is. This is what you'll be trying to get on if all else fails. Keep an eye on the GA and check in INfrequently. At this point, it can go one of a couple of ways:

1) If they ask for volunteers, you'll generally be first pick. Freebie ticket! Awesome. If they say that you'll have to stay overnight, repeat after me: "Is there anyway I could get home tonight?" In my experience, GA appreciates you being so helpful and will be helpful right back. Last time I did this I went from E+ on the first flight the next day to F on the next flight 3 hours later... along with the free ticket.

2) They don't need you at all. Oh well. You still have a shot at being bumped to F if you're damn lucky and don't come off as expecting something... Wait and let the other people board, and talk with the GA that you've been talking with. Say something like, "Well, I guess you didn't need me tonight. Have a great night". If you're damn lucky, they might.. I stress MIGHT (MIGHT!)... be nice enough to do a little extra something for you. In the past, the GA has pulled me aside, taken my blue boarding pass, handed me a new gold pass, and told me to have a nice flight.

3) They don't need you, you talk with the GA and they just tell you to have a good flight and thank you for your help. You go sit in your Y seat and call it good. No upgrade for you.

Again, the point of all this is NOT TO BE AN EXPECTANT JERK. If you EXPECT an upgrade, the GA is less likely to upgrade you. It's a truism of the service industry: The more you demand special treatment the less motivated the person helping you is to give you special treatment unless your status absolutely 100% requires them to (like if you're the CEO of UA). If you are NICE, HELPFUL, and FLEXIBLE the GA has an easier time doing their job and as someone who takes stress out of their life, they are more likely to take some stress out of your life by giving you a seat in F to show their appreciation -if you are lucky-. Sorry for the caps there, but I wanted to stress the not being insistent or demanding. If everyone starts doing this and doing it poorly, the GA's might get jaded. So, use in moderation and only when the plane really looks full! And again, BE NICE FOR THE LOVE OF TRAVEL!