to do or not to do... bulbs

Do you pull bulbs and winterize them or do you leave them in the ground?

I've found that if I leave bulbs to their own devices they start to multiply on their own. As the years go by you'll have more and more flowers.

The downside is that if you have limited garden space you won't have a lot of room to plant other things during the summer if you leave in the bulbs.

The first couple of year I left them in, then last year I wanted more space to I dug them out. I didn't do the regular recommended winterization and to my surprise they started to sprout again in their paper bag. I replanted them all this season, but I'm debating about removing them again once they have flowered....