Sequels can serve a purpose if they're planned out from the beginning. Take Harry Potter for example... each book covered a specific year of Harry's schooling, yet each was a completely different story in addition to building the world she created.
Sequels that exist just because the franchise wanted it go off the rails... take Star Wars for an example. They should've stopped after Return of the Jedi but once the almighty Mouse got involved, greed took over.
I enjoy having characters cross over and make an appearance in another story, but they're not the feature. Its like running into an old classmate... you smile and say hi, maybe exchange some pleasantries and then move on.
The only series I did, I didn't want it to be three stories from the same character's perspective. Each story featured a different main character pair, but the plot itself built up within each one.
It doesn't make sense to continue a particular story if you've covered everything you wanted to in the first one.