When I was growing up, my mom had wrapping paper for EVERY occasion. Christmas, birthday, wedding, baby shower, etc. And we had a huge box to store it in... and shopping bags of FULL of beautiful, shiny wrapping paper that didn't fit into the box... plus ribbon. You get the idea.
I don't have the room to store so much pretty wrapping paper (sigh), so I have to take a different approach that actually saves me space AND money on wrapping paper. When it goes on sale after Christmas, I buy the stuff that's pretty that doesn't scream "holidays". Generic metallic stripes, glittery polka dots or solid papers. Then, I can pair them with different colored curly ribbon to fit the occasion. Curling ribbon is available in TONS of colors at your local craft store and online at uline.com.
I have three or four colors of the ribbon to coordinate with my wrapping. It's easier to store than the puffy (crushable!) ribbons, but can be just a pretty when you get to curling!