bad idea for two reasons if it's pre 90's it might have asbestos if it's pre 80's it will have asbestos. And second the texture that will be left will not be pretty

Easier to drywall over it !! More expensive, but easier.

jan usually gives wonderful advice but not this time. ; )

test for asbestos if its an older home, but Just Do It as far as the popcorn removal. nice smooth ceilings will make up for 3 other unattractive things you have going on that can't so easily/inexpensively be changed, and if you have no other unattractive things in your home, why ding it with a textured ceiling?

Leaving some texture will just be leaving a mess

I've removed popcorn ceiling from two homes, and in my experience it is definitely worth it! I agree with Rhoni though, it is very monotonous to leave texture. I would wet scrape it then sand and paint over it after.

This article has some good tips if you're planning to DIY. If you get a large blade and attach it to a pole it can make the process much simpler: http://www.wbdoors.com/blog-layout/the-popcorn-ceiling-removal-saga-and-4-videos-to-make-it-easier

I have dry scraped the popcorn off in many rooms in my house. Use a 6-inch putty knife, round the corners with a grinder to prevent cutting into the sheetrock. It will leave a nice orange peel type surface that can be painted with some flat white Behr ceiling paint. You will need to buy some plastic painting sheets to cover everything in the room, because dust will be everywhere. Also, carefully vacuum ceiling when done, and get a bag for your shop vac, you can thanks me later on that one.