Where can I find references that discuss important classes of Infinite Hopf Algebras. By important classes, I mean heavily used in research and of relevance to Hopf Algebraist(s),Physicists, Analysts(Real/Complex),..etc.
Shahn Majid's book Foundations of quantum group theory (Cambridge Univ. Press 1995, 2000) has lots of examples and of classes of examples. These are not only examples of quantum groups in the narrow sense (cf. the $n$Lab page for other references on quantum groups in various senses).