Out of the various "Orthodox" groups, i.e. Litvish, Chassidim, Sephardim, Yemenites, etc., do any of them forbid marriage to the other?
No there is no prohibition to marry between these different groups.
As long as they are from a kosher Jewish lineage (not offspring from a forbidden relationship, come from a Jewish mother etc.) there is no prohibition to marry them.
Regarding Chassidim, there was a ban issued by the Vilna Gaon against them which included a ban in marriage. However this does not apply nowadays.
There are cultural and Halachic differences between them, which may lead to more marriages from "within".
I once heard from a great Rabbi that "marriage is hard as is, no need to make it harder by marrying someone from a totally different cultural backround"