A label isn't always necessary, but it can be helpful in addition to an animation.
If it's an extremely brief action, just a loading icon/bar might suffice. When you're performing multiple "loading" tasks some descriptive text can help.
A great example is Google Currents. When opening an already downloaded "issue" in Currents, you get a textless loading animation for maybe half a second. It's so brief you don't really need a loading icon.
However when Currents is downloading an issue, it says "Fetching current items..." to let you know it will take longer. It also gives you the option to cancel this step and read the old issues, and the cancel option wouldn't make much sense with no loading text.
Never use just a static lable, because as AndroidHustle notes, there's really no visual indication that anything is working. The animation is in no small part to help you see that the page isn't frozen.