I removed all the artex from my 30s semi.
DONT use a wallpaper stripper, it makes a total mess.
Some pre 1980s Artex contains very small amounts of "heavy" asbestos, you can see it as small silvery specs in the dust. I have read that the levels of asbestos are not going to kill or do anywhere near as much damage as insulation / roofing / blue etc, and as it's heavy dust it can be vac'd up with a HEPA vac or dyson. (Disclaimer: I believed this and I may die from it in 20-30 years time so don't believe everything you read!)
Most of the artex I removed came off the underlying lining paper or plaster really easily using a jumbo scraper which you can get for about £6 - long handle with a big h/d razor blade on the end - works a treat!
For really tough areas including some of my ceilings I hired one of these babies:
[DLMURL="http://www.hss.com/g/5231/Drywall-Sander-Kit.html"]HSS Hire › Drywall Sanding Kit[/DLMURL]
If you go down the messy route make sure there are no kids or pets in the house. Wear a good mask FFP3 minimum and goggles. The dust gets everywhere so seal rooms and wear paper overalls.
This was before I learnt to plaster. Now I just scrape off the bumps with a clean trowel edge, couple of pva coats and skim away - easier and cleaner.
as a plasterer..i'd say give it a good soaking and start scraping..wallpaper steamers as all ready mentioned work well. As dh says if painting knock off the highspots and re-skim, if tiling i'd scrape on a day rate...I wouldn't be confident of re-skimming and then tiling..although it does stick like the preverbial to a blanket..Mark.