Since teabags were invented by Thomas Sullivan in 1904, the debate has raged on: Bag or Loose?
Certainly, for convenience, teabags win out everytime. Individually wrapped, they can be carried about, and all one needs is a cup of hot water. Loose leaf tea is certainly more inconvenient, and can be a bit messier. Strainers or infusers must be rinsed and leaves discarded. So what advantage does loose leaf tea over bagged tea?
The answer is simple: flavor. But why? First of all, to get the full amount of flavor from tea leaves, they must have room to expand fully. In the case of oolong teas, the difference between the tightly rolled dry leaves and the unfurled steeped leaves is quite dramatic. If they are unable to unfurl, some of the flavor stays trapped within the leaves. Ideally, the leaves should be able to swirl freely in the water in which they are steeping to get the full flavor.
The second reason is because of the size of the leaf. The smaller the leaf, the more quickly bitter tannins are released, and the more quickly tea becomes bitter. Most loose leaf tea is whole leaf, while tea bags are filled with fannings, or tea dust from the bottoms of crates and barrels of teas. Basically, the cast off bits of tea.
Teabags also tend to go stale more quickly. Tea can stay fresh for up to two years, if properly stored in an airtight container and kept in a cool, dark place, like a cabinet. Teabags are frequently improperly packaged for freshness. Celestial Seasonings, for example, has the teabags loose in its paper boxes, so no freshness is preserved at all.
For these reasons, given the option, I would take loose leaf tea everytime, and it is most frequently what I drink when I am at home, or if I have my Nissan Thermos with me, with its handy infuser. However, on airplanes and in restaurants, these options aren't practical.
So, if you must use teabags, what do you look for?
The most important thing is packaging. Make sure that your tea is going to be as fresh as possible, so avoid any tea that is solely packaged in paper. Tazo and Celestial Seasonings are the most common culprits. Twining's is slightly better: the bags are packaged in plastic wrappers. However, once you open the plastic, put the teabags in an airtight container, separating flavors. Bigelow is the best of the traditional bagged teas, as each teabag is individually foil wrapped. Ashby's are also individually foil wrapped. However, in recent years, as tea has grown in popularity, tea companies have experimented with ways to combine the best of both worlds, and whole leaf tea is now frequently available in infuser bags that allow more room for the leaves to unfurl. Adagio, Revolution, Mighty Leaf, and Two Leaves and Bud are four companies that market tea in this fashion, of which Revolution is my favorite brand.
Revolution is great, because although the outer packaging is paper, the inner packaging is a resealable plastic container.
Adagio is also amazing, and very reasonably priced for both loose leaf and bagged tea.

Remember again, no matter in what form you infuse your tea, keep in in a cool, dark place, in an airtight container, away from strong odors. And enjoy!