Internal martial arts can be defined as those which rely of the use of qi rather than muscular strength (li) to power the various strikes and blocks. Like most things Chinese this is an oversimplification. The three great Chinese internal martial arts are Tai chi (taiji), Bagua (Pa Kua) and Hsing Yi (Xing I). All of these arts claim various sub-styles that are accepted by the martial arts community as a whole to a greater or lesser degree.
Liuhebafa is a Martial Art which has combined all three of the great internal arts to form a very large and purportedly flexible system. It is my impression that liuhebafa is generally accepted as a legitimate martial art.
A 5th Chinese Martial Art that is considered to be internal is I Chuan or Dachenquan. This art seems to have discarded fixed forms in favor of a very free form ad hoc approach to fighting. This seems to be an accepted internal martial art by the community.
The other martial arts listed in the right sidebar of this page seem to be generally less accepted as legitimate internal martial arts. Mr. Tak Wong has sent me in an email his opinion of these arts .
"WuJi Quan was a scam. It was associated with some Buddhist cult during WWII in ChungKing. San Pan (3 stances) Shi Er Si (12 postures) are basic practices in Liu He Ba Fa, which was basically a ripoff of YangTaiJi by Wu YiJun around the turn of he century. TaiXu Chang Quan was a "ShaoLin" style. It was mentioned in the Journal of Lao Zhan, a very popular novel by the Qing author Liu O (circa 1880). This book is a standard Chinese literature text in most high schools in Hong Kong and Taiwan. It really stretches the mind to associate Tai Xu Chang Quan with internal martial arts. Don't know what Da Bei Quan is. Ba Ji (Rake) Quan was named as such because the practitioners held their fist semi-openly, like a rake. To many Chinese practitioners, "Rake Martial Art" sounded so rustic and unsophisticated. Therefore, they started using a phonetic equivalent which meant 8 Extremes, which has nothing to do with the style itself and confused the hell out of a lot of people because it sounded close to TaiJi - the ultimate extremes. Maybe that is the reason Westerners think it has anything to do with internal martial arts. Don't know what LaiJiaQuan is. Zhang Song Qi was a well-known "WuDang" boxer of the Ming time - circa 1600. The WuDang 32 Long Fist has been attributed to him by some practitioners. The 32 Long Fist, of course, was the precursor of Chen TaiJi. I have heard some years ago, some Mainland Chinese practitioners came up with a new style attributed to Zhang Song Qi, and hoped to hand it off to outsiders as "genuine internal gong fu". I think this SongQi LeiJiaQuan is one such product. Don't know what TamBeiQuan is."
Paul Martinez, who provided me with the Baji URL's, also questioned whether Baji should be considered an internal art. Otherwise the sites he provided are consistent with Tak Wong's comments above.