I live in Southern California, where the "cottage cheese" ceilings were all the rage a few decades ago. I just moved into a "new" 35-yr. old house, and I want those smooth ceilings, too. The key to getting the stuff off is getting it wet (use a spray bottle), let it sit for a few minutes, and then get to work with a 12" scraper, being careful not to gauge the ceiling panels underneath. If you're dealing with an older home, the texture may contain asbestos; in that case, I'd recommend using a contractor to strip it. Either way, you'll probably want to consult with a contractor to finish the ceilings; scraping will expose the drywall seams, and you'll need to hand-cover the ceiling with a thin layer of putty and do at least a few sandings to get that perfectly smooth look. It's pretty labor intensive, so it'll cost bucks and time if you are committed to a 100% smooth finish.
Another option is to scrape the existing stuff and reapply a light texture, similar to what a paint roller leaves. This is less noticeable and costs about 50% less if you're contracting it out, at least based on the estimates I got for my place.
If you're doing the job yourself, be sure to cover EVERYTHING with plastic & tape (unless you just LOVE dusting and vacuuming), and wear a mask and eye protection. If you're dealing with asbestos, be sure to get a mask with a respirator; that stuff is nasty, and you can't just throw it in the trash these days; you'll have to take it to a hazmat waste site. Call your local disposal co.; they should be able to refer you to one nearby.