To supplement the above info, a few styles (of Southern Shaolin arts) that may have been left out:
TaiZu Quan (grand Ancestor Fists)
LuoHan Quan (Bhoddidarma)
TaiZu is supposedly founded by the Southern Sung emperor. t was 'designed' for military use, i.e.: smile and effective. It is based on the principle of using the arms as 'blades' with thrusts, slices, chops. The movements tend to be more short & linear than circular, suitable for use with armour.
LuaHan is attributed to Bhoddidharma, the Indian monk who brought Buddhism to China, Also the founder of Zen Buddhism and of Shaolin. It is more well known for developing internal energy than as a combative martial art, although it is highly effective in the hands of an expert.
WuMei (or NgMui) was a legendary nun at S. Shaolin, reputedly also the ancestral founder of WhiteCrane and WingChun. It is a rare art, with emphasis on development of internal energy, but with combative applications. Unlike the northern internal arts, its forms are done fast, not slow.
Also less well known are the Hakka styles, Ngok Gar. etc...
There is a distinct difference between the Northern and Southern arts as mentioned above. The reason for this is environment and physique. Northerners tend to be physically larger compared to southerners. Also Northern China is grasslands and semi-arid plains, whereas Southern China is hilly, forested or wetlands. Hence Northern cities and countryside have open spaces; favouring long movements and weapons. Southern environments include narrow city streets, mountain paths, boats; lending itself to short, close quarter techniques and firm (but mobile) stances. Hence even within Shaolin, they are different; e.g there are northern and southern versions of LuoHan and TaiZu.
WuZu Quan or 5-Ancestors Boxing is allegedly created by the 5 monks that escaped the destruction of the Northern Shaolin temple and fled south. Each was a specialists in one of the 5 styles; Monkey, White Crane, TaiZu, LuoHan, Da'mo(Bhodidarma) and they combined the best features to create WuzuQuan. Because of the combination it has a wide variety of techniques, which makes it harder to learn. It has both internal and external aspects. The QiGong part is important, so is conditioning of fists, fingers, forearms and legs. (disclaimer: this is the art I'm involved in for the last few decades). You can find out more on Wikipedia, although that's not exactly our lineage.
TaiZu, WhiteCrane, Wuzu are considered Fujian arts (originating form Fujian province/state) and are still widely practiced in Fujian. OTH WingChun, HungGar, ChoyLiFut are considered Cantonese arts.
BTW the Northern Arts of TaiJi, BaGua, XingYi are WuDang/Taoists arts, not Shaolin. Shaolin is considered Buddhist, and there were rivalries between the two.