You can feel transformers from a (comparatively) massive distance away: I can feel a 230-to-12V transformer from 5 to 10cm, which is generally bigger than the transformer is. So you'd know to steer clear. I mean, IAmDann said here, http://www.reddit.com/r/IAmA/comments/g7lom/iama_24_year_old... that he can feel subway power transformers while walking down the street.
Demagnetizers... isn't the whole point to enclose the field? I'd also expect a warning sign or two, or for you to pay attention and know it's there. This is one of those "make your decision, and then live with it" things, and part of "living with it" is being aware of these things (and that acquaintances with more humour than sense might try to hand you magnets you can lift tables with).
Large electric motors... Dunno, have no experience of them yet.
Do you get a sensation from switching power supplies vs transformers? Or is the frequency in a switching power supply too high to sense? (I've been studying power supplies a lot lately, so I'm curious.)
Tangentially on the topic of MRI safety, there's a fascinating story of a police officer who got too close to an MRI. The magnet yanked the gun out of his hand and the gun went off despite the thumb safety being engaged. (Nobody was hurt and the MRI received only superficial damage.) Apparently the strong magnetic field pulled the firing pin block out of the way, allowing the gun to go off. Details: http://www.ajronline.org/content/178/5/1092.full
Thinkpad switch-mode power supplies give almost no sensation, but I have gotten a distinct (and pretty distinctive) "buzz" from a Dell power supply. I'll point out others seem to be much more sensitive than I, as well (see jaa's comment, below; he can feel power cables. I can't). So the answer is... it depends? ",)
I once broke my finger handling magnets from a really old hard drive. I don't want to think about what would have happened if I had magnets implanted in my fingers.
They're rarely as strong as MRI magnets. My sister, who works as MRI technician, have seen MRI pulling with a blazing speed whole wheelchairs or heavy steel oxygen canisters from many meters away.