Even if you are okay with the fact that you're single, hanging out with a couple can be awkward. If you find that spending time with friends who are romantically involved makes you uncomfortable, it's time to look at what's going on with both you and your coupled friends in order to ask why. By figuring out where that pesky “third wheel” feeling comes from, you can figure out what to do about it.
When It's the Couple's Fault
Sometimes there's nothing you can do about feeling like a third wheel...if the problem stems from the couple. Some people are adept at social interaction as a couple, but others struggle with remembering that there's a world outside the boundaries of their relationship. If they're so into each other that you feel like you're invisible, or if they're sniping at or arguing with each other, you've become a captive audience for their private issues. This is uncomfortable, and there's nothing wrong with calling them out on what's making you uncomfortable or removing yourself from the situation.
Healthy Couple Dynamics
Spend time with couples who have a healthy relationship dynamic when it comes to socializing. Bear in mind that, in some cases, this can be a matter of waiting for a couple to get to this point, whether they're ending a rough patch or just getting through the “honeymoon” period. Spend time as friends with coupled people who know how to put up a barrier between socializing and private interaction. This doesn't mean that a healthy couple will show no sign of being romantically involved when you're around, but they should keep it subtle and casual. Most important, they should pay attention to you, make you feel welcome and demonstrate that your company is enjoyed and appreciated.
Avoid Third Wheel Situations
One of the best ways to avoid feeling like a third wheel, of course, is to not be one. If you find that every social situation you end up in with a couple is uncomfortable, consider inviting another friend, or even another couple, to come along. It might be easy for your coupled friends to leave their bad behavior unchecked when just one person is around, but having other people on your side is likely to remind them of what's appropriate.
If you feel like you are, or could be, good friends with both members of a couple separately, strengthen your friendship with both people individually. Look for opportunities for one-on-one outings with both members of the couple to build your connection and comfort level. This improved dynamic will equalize things a bit; not only will the couple have a close connection with each other, they'll each have a close connection with you, making it more likely that you'll interact as three separate individuals, rather than two plus one.