It's a bit gimmicky, but I wonder if it's possible to make a purple beer? Food Coloring only works for "hard" food, but I've never looked into coloring beverages and I don't want to affect the taste and create something as horrendous as Crystal Pepsi.
I imagine it depends upon the type of coloring - some food coloring can also work in liquids - just try dropping a few drops in a glass of water. With beer, you may need a lot of coloring for it to influence the beer color significantly.
Depending upon the beer style, you can also color with fruit juices, but of course these will have some affect on the flavor. For example, you could make a purple hefeweisen by adding blueberries in primary. I once made a cranberry hefe for halloween, which had a blood-red tinge to it. Cranberries are quite sour so I didn't want to add too much - with blueberries you could use more.
Ordinary water-based food coloring works fine. I once made a green beer for St. Patrick's Day by brewing up a simple ale and then adding in yellow and blue food coloring after primary was over until it was green. I would stay away from food products initially, because some of them (like fruit) can influence the flavor as well.
One thing to remember is that the starting color of the beer will GREATLY affect the final color after the additives. If your beer starts out Pale Yellow, for example, then you might just want to add a little Blue to make it Green in the end. If your base beer is anything darker than an IPA, you are going to really have to play around to see if you can hit the final color. I would suggest pulling out a half pint or so, and adding the dye in very small amounts to see if the final color is even possible. For example, I doubt you could ever make a beer Blue unless it was incredibly pale to begin with, since adding Blue to even the palest beer would probably make it Green.
Colors that are based on starting with Yellow or Red seem more probable. You could probably turn a pale beer Orange with a little Red, or maybe turn an amber beer purple with a little Blue.
I definitely know that it is possible, but I don't know how to do it. I was in a pub that served green beer for St Patrick's Day, so I know that it can be done and it has been done. I assume that it is just food coloring, but I've never done it myself. I would imagine that you would need a light colored beer like a Pilsner which has also been filtered (I don't even use whirloc in my brews). Also, I would assume that you would do it to the finished product and not to the wort. But I've never done it, so I am only guessing.