Most airports now have self-check-in kiosks that have cut wait times considerably. But during high-traffic times -- e.g., the holidays -- waits to use them can be interminable, especially when half of the machines are mysteriously down. Most airlines allow you to check in online and put your boarding pass on your phone. So if you're only carrying on, you’re all set. But even if you’re checking bags, the skycap and a few bucks will get you past the herd.
Avoiding this line is strictly a matter of choice. For some reason only stand-up comedians understand, people crowd around boarding gates as soon as the gate agent picks up the PA system, as if their seat will be snapped up if they're not first on the plane. Then they mope down the jetway while people try to figure out where 24C is. Some people do this because they fear the plane will run out of bin space, and they'll have to check their bag. Even if that does happen, though, the bag fee is waived. So, really, you have no good reason to suffer through this.
Your best move here is to just sit back, nurse your beer at the airport bar, finish charging your phone, and board the plane dead last. Or just enjoy the Airport Channel until it looks like everyone else is on board, ensuring you get there before the gate closes. If that’s just too anxiety-provoking for you, many airlines offer credit cards with perks that include advance boarding. And if you're a frequent flyer, elite-level program members board first as well.