There are several champs that you can't pick just because they're banned so often, like nocturne, zilean, shen, and eve. My five would be:
Warwick- most versatile jungler, never banned.
Kennen- rarely played champion that can be viable as ap, ad or tank, depending on how you build him
Sion- again, really flexible, can fill multiple roles (even jungle in a pinch) depending on how you build him
Alistar- another flexible champ (getting my drift?) who can play either full tank, dps/tank hybrid, or ap. Aoe disables ftw.
Ashe- her ult is just too good to not be able to use