Brown Porter is the lightest of the three varieties, and generally has an alcohol content of 4-6%. Brown Porter is still more popular in England than in the US. It is light brown to dark brown in color and has almost no hop character. It will be light to medium in body. It may have a very light roastiness to it, possibly accompanied by some biscuit or chocolate notes. Samuel Smith's Taddy Porter is a good example of this style.
Robust Porter is a later development, and is Brown Porter's bigger, stronger brother. It's more popular in the US than in England. American brewers are always pushing the limits, and their Robust Porter varieties are a good example. We use everything from Maple syrup to Vanilla to flavor our Robust Porters. A Robust Porter usually is stronger than the brown variety, with an alcohol level of 5-7%. It is also darker, and roastier than it's little brother, with more hop presence. It is usually dark brown to almost black. Black patent malt is one of the ingredients common in this version of Porter. Anchor Brewing makes a good example of a Robust Porter.
The final version of Porter that I will mention is Baltic Porter. A Baltic Porter generally comes from one of the countries bordering the Baltic sea, such as Poland, Latvia, or Lithuania. Of course, there are some American brewers who are copying this version of Porter as well. Baltic Porters seem to have been influenced by Imperial Stouts, since they are bigger and sweeter than Brown or Robust Porters. A Baltic Porter may have a wine-like character, due to its higher alcohol levels - up to 10%. It will have very little hop flavor, and may be heavy in chocolate and sweet malt character. Like the Robust Porter, it is also very dark in color, possibly black with ruby highlights. Zywiec Porter, from Poland, is one of the better known Baltic Porters. Utenos and Aldaris are two other Baltic Porters.
Finally, here is a gratuitous picture of my Dachshund, Porter who hasn't got a clue about the origin of his name.