So here are some potential ideas of how you could potential modify characters to fit into a single Universe.

[list][*]The Thundercats could be used if we changed the time period they were in.  They could crash land in some uninhabited place like perhaps the African Plains or perhaps the Cascade Mountains and have to get used to their new life on Earth.  The fact that they would be in a modern day earth rather than a post-apocalyptic one would completely change their story arcs.  Perhaps they would try to integrate themselves or at get to know humanity.  Mumm-Ra would probably be asleep at first but could be woken up by the Thundercats somehow.
[*]Something like MegaMan could easily be modified to fit in a shared world.  Pretty much just have to drop some of the world lore to make it fit in a shared universe, pretty simple.
[*]Generator Rex would need a serious overhaul to the backstory and have a much more localized nano disaster so there wouldn't be as many EVOs to contain and cure but could still have trouble with the main villains, perhaps trying to spread the nanobots to the entire world, or just do regular hero type stuff.[/list]

The main point is you need to come up with a way to safely integrate the character into a shared universe setting that is similar to the real world, or at least a comic book world that is based on ours.  A lot of shows might have mechanics or lore that really wouldn't work well in a shared universe so you will need to either modify it or find another source of inspiration.  In general, try not to use a character from a world too far advanced to mesh well with a more present society, or a character where the needed changes to fit would kind of destroy their identity.