While there is no one who is not allowed to get married (at least at first), there are some people r”l who have an extremely limited choice of whom to marry. For example, a mamzer cannot marry anyone other than a mamzeres or giyores. Similarly, there are also certain physical problems which prevent them from having children(of which I have never heard about in the current day, but they theoretically do exist) who would be bound by the same limitations. The Gemara in Yevamos (eighth perek I believe) goes through who this would apply to.
That being said, I can’t think of anyone who is never allowed to get married (with the possible exception of a kohein mamzer).