I store things I don't like, such as all three CoC castles; things I've got as prizes or in Mystery Boxes where there are enough of them in my town already (eg hovercopter, I've got two but only want one; topiary angels, got three but only want two, one for each side of the church); out of season things, like easter eggs and halloween pumpkins; and bits and pieces of fence, walls, barricades and stop signs that have accumulated during remodelling efforts.
And also Mr Teeny. He drove me mad with his single task that required Krusty to be free as well. He'll be in storage forever.
Otherwise, my town is not yet so full, nor my coffers so rich, that I want to store buildings (other than the castles) or any item with a multiplier. If I don't want to see a multiplier decoration I'll hide it behind a building (eg cornucopia, hidden because it's out of season now, but next Thanksgiving I'll put it back in Springfield Park).
I haven't stored any of my NPCs yet, so far I quite like most of them. Bonestorm Santa will have to go at the end of the holiday season, and the Capital City Goofball might go as well. I feel that he has no business being in Springfield.