Although "Hoover" is sometimes used as a synonym for a vacuum cleaner, particularly in BE, it is not correct to use unless that appliance is actually made by the Hoover company. (Hoover is a registered trademark in the U.S.)
Common usage, however, has a way of overwhelming technicalities. Sometimes trademarks become synonymous with the product, e.g. Kleenex, Linoleum, Thermos, Xerox, Teletype, etc. Sometimes these companies fight public relations battles (usually hopeless) in an attempt to educate the public that these names are indeed trademarked.
If you were going into a shop to buy a vacuum cleaner and asked for a hoover, they would show you the vacuum cleaners made by the company Hoover and not any others. If you want a Hoover, then it's a good word to use, otherwise it would be best to just say "vacuum cleaner".
Hoover as a generic term for a vacuum cleaner is alive and well in the UK, as is the verb "to hoover".
A quote from a UK blog, dated 11 Aug 2007: ... at times I've had older children hoovering, having borrowed from the janitor. Currently we get the hoover and do it ourselves if things are get really bad
I'm willing to wager that the writer did not check the brand-name on the machine.
In this blog entry, from Jan 2006, the writer is actually discussing a particular vacuum cleaner, made by Morphy Richards, and uses "hoover" as a generic for vacuum cleaner. I e.mailed Morphy Richard 2 weeks after I bought it and voiced my concerns about the hose and was told that most people buy a cylinder hoover for hoovering at any distance.
In the UK, hoover is also used in extended senses: I never bother sweeping the floor when my brother comes round, because his dog will always hoover up the crumbs for me; ...vacuum up ... would not fit so well because it might imply that the dog gets the vacuum cleaner out.
Do Hoover still make vacuum cleaners? I haven't seen the Hoover symbol on one for years!
They're also available in Australia (I just checked a few on-line shops to make sure I wasn't imagining it! Also, Hoover vacuum cleaners have an Australian web-site, under the title of Hoover Floor Care.)