Historic Founder Chang San-Feng (Taoist)
Chen, Yang, Zhao Bao, Yang, Wu, Wu/Hao, Sun and there is a Li style as well. Not to mention several others I cannot remember the names of or I don’t know the names of. There can be big differences as well as similarities between the family forms
Chen, Yang, Wu, Wu/Hao, Sun are the 5 families recognized by the Chinese government as Tai Chi Families. I recently heard that they may have just recognized Zhao Bao as well.
Chen family came first (if you believe the Chen family history, but it was before the other family styles) Chen has and still teaches both Old frame and new frame and has lower stances than Yang style. I have to admit I like Chen; it still has obvious applications, Qin Na and fajing in the forms. Current family head is Chen Zhenglei. He is very good and very skilled.
Yang came from Chen
The most popular style today is Yang from the Yang Cheng Fu line. However there is another line, not as widely practiced that comes from Yang Chengfu's older brother Yang Shouhou (also spelled Yang Shao-hou) and uncle Yang Binhou (also spelled Yang Pan-hou). Yang Chengfu changed the form by removing the much fajing and Qin Na. However he did create a fast form (Yes there are fast forms in Tai Chi)
Current head of family style is Master Yang Zhen Duo and I believe the next in line is his grandson Master Yang Jun.
Zhao Bao came from Chen and is very cool, very low, very powerful
Wu Came from Yang, Pre Yang Cheng Fu
Wu/Hao also came from Yang, also pre Yang Chengfu
Sun Came from Wu/Hao. But the founder of Sun was considered a master of Xingyi and Bagua. There is a very good Xingyi book by the Sun founder Sun Lu Tang. Just as a side note Sun Lu Tang daughter and Sun style family head just died last year.
Zhao Bao is very rare and hard to find it may or may not be a combination of Chen and some other martial art from Zhao village. But it historically comes from a Chen family member.
Li style I have never seen, but it is also a combination of Tai Chi and other martial arts like Sun style.
Dong Style is from Tung Ying Chieh, a student of Yang Chengfu. However I do not think Sifu Tung ever called what he taught Dong style. I believe that came from either his son or grandson. Tung Ying Chieh added a second fast form and possibly a second straight sword and broad sword (da dow) form as well. Sifu Tung allegedly studied Wu/Hao prior to studying with Yang Chengfu and there are even some references that he may have studied with Yang Shouhou prior to studying with Yang Chengfu
Be very careful about Yang style classes or any Tai Chi classes for that matter. Many are not the full family forms. If the Yang class is in Yang 24 and 48 it is not traditional Yang. These are government competition forms. Most unfortunately all the 5 families have government competition forms. These forms are not generally taught be the families. Also depending on what you are after with Tai Chi, health and fitness, martial arts or both. It may be difficult to find an actual Martial Tai Chi School. Most are now for relaxation and health. However Zhao Bao I doubt has gone that root yet. Yang certainly has, Chen may be and I am not sure about Wu, Wu/Hao or Sun. By the way traditional Sun is also rare.
Also lineage is a good thing but not the end all be all of a good teacher. I know of bad teachers with good lineages and good teachers with less direct lineages. But in general lineage can be a good thing.
Links of interest
http://www.chebucto.ns.ca/Philosophy/Taichi/styles.html
List of Tai Chi Chuan forms
http://www.answers.com/topic/list-of-tai-chi-chuan-forms?method=22
Chen style
http://www.answers.com/Chen style Tai Chi Chuan
Yang Style
http://www.answers.com/Yang style Tai Chi Chuan
http://www.yangfamilytaichi.com/
Wu/Hao Style
http://www.answers.com/Wu%2FHao%20style%20T'ai%20Chi%20Ch'uan
Wu Style
http://www.answers.com/Wu%20style%20T'ai%20Chi%20Ch'uan
http://www.wustyle.com/
Sun Style
http://www.answers.com/Sun%20style%20T'ai%20Chi%20Ch'uan
Tchoung Style (this is a new one on me)
http://www.answers.com/Tchoung style Tai Chi Chuan
Dong Style
http://www.dongtaichi.com/
Tai Chi History
http://www.chebucto.ns.ca/Philosophy/Taichi/history.html