Overlining slows the rod action down a little, and that can be a good or bad thing depending on what you're trying to do. I have a 7wt rod that I overline with an 8wt line to use for sightcasting to redfish from my boat. Fish that you can see are normally fairly close, so the casts are shorter. You need the rod to load quickly and with less line outside of the tip, and so overlining works well for me in that situation.
On the other hand, if maximum distance is your thing, such as when blind casting, then I'd stick with the normal weight line for the rod.
Like Bruce said, it depends on what you have and what kind of fishing you do. As a rule, you can go up one line weight and down one line weight. If you find that where you fish doesn't require long cast and finesse presentation then you can overline and chunk a bigger fly or make your cast faster. If you try to cast long you will have to slow your timing down some because you will have the rod loaded plus some which in effect makes the action slower.
The website listed below has quite a few in depth documents that might help clarify why you might want to over line or under line a rod from a technical perspective.
This might be more info than you wanted, but I found it about a month ago and thought it was really interesting. If you are not really into this kind of stuff, it can also be used as a cure for insomnia.
i over line my rod when the wind is blowing to get maximum distance. i have 3 reels and 1 is under 1 is right and 1 is 1 weight over to cover any situation i need. the 1 that is under i can cast further on very calm days. the 1 that is over i cast further on windy days. i know i could just buy extra spools and use them . but i like reels and the more i have the more happy i am. a fast action rod is best for overlining your rod since you can feel it loading up and it takes less false cast to get the job done. JMO randall