I use a section cut from a plastic coat hanger in a sort of J shape, chucked in a cordless drill at low rpm, to degas. I submit that I am not introducing any oxygen at all into my wine by using this method, since the wine is in a carboy and any headspace is actually filled with CO2 gassing off the wine in the process.
It's not necessary to "whip" the wine to get the gas to move off. All that's needed is to move the liquid enough for bubbles to form.
Everyone who has mentioned it so far is absolutely correct, if you age it out for long periods the wine self-degasses. With my higher-level wines this is my preferred method. Because I make a wide range of wines, I don't always want some grades to take up carboy space that long.
There is a second method that is also effective, called sheet racking. In this, you place the end of your racking tube into the new carboy high at the top so that the wine racked over sheets down the side of the new carboy. Gas is released from the sheet and quickly fills the empty carboy space with CO2. I have also used this method, which I learned here. It is probably best for bolder wines, and not for the more delicate bouquets and flavors. The advantage is that you degas as you rack.