BS”D
In all seriousness, few if any Chassidishe rebbeim are descended directly from the Baal Shem Tov. Reb Nachman meBreslov was married to a descendant but of course the line died out. I think there are other lines direct from the Baal Shem Tov but I am not sure which they are and whether they survived to this day.
Most are descended from one or more talmidim of the Baal Shem Tov or the Maggid. Reb Nochim Chernobyler (Twerski) was a talmid of the Besh”t – his descendants include all of the Twerski rebbeim of today, including Hornesteipol/Milwaukee, Rachmistrivke, and Skvere. (And of course everyone’s favourite Skverer, Lipa, is proof that Skvere comes from Chernobyl…AFTER the nuclear accident!)
The two Satmar rebbeim are descendants of the Sanzer as well as..the Baal HaTanya (Alter Rebbe of Chabad)! This means they are related to Bobov and Klausenberg as well as indirectly to Reb Michel Twerski.
Others are descended from talmidim of the second generation after the Besht (talmidim of Reb Elimelech for instance). And Rizhin is descended from the grandson of the Maggid; many Rizhiner offshoots such as Boyan are alive and well today.
I think the only Rebbeim whose yichus does not go back to that time are the Toldos Aharon and Toldos Avraham Yitzchok except perhaps via marriage. Reb Arele (Roth) founded the original Shomrei Eminim rather recently.