I've got an old house with some asbestos tape on the heating vents, and some old floor tiles which are asbestos suspects as well; duct cleaning firms won't do cleaning on the vents with the tape present. Do I really need to call in the space suit guys to get rid of it? If I just cover it with new foil tape, will that encapsulate it safely? Should I just rip it off myself?
It's not really that serious in most cases. In tile or siding, it isn't a hazard unless it is broken down, generating dust that you are breathing. Even then, a lot of tile is like 1% asbestos. If you can get it up without breaking it too much, you're basically fine.
Pipe insulation that is soft is more of a problem. You can probably do it yourself if it's a small amount. It may very well be illegal though. Get a respirator like this http://www.amazon.com/MSA-Safety-Works-817664-Respirator/dp/B0009XW3ZS, take a heavy plastic bag, tape it around the insulation so it's mostly sealed, and then spray it down with water so it's saturated and won't generate dust. Then remove it, dousing with water as needed. Seal it up in the bag and dispose of it lawfully.
I was an asbestos abatement hygienist for 3 summers, and I took airborne fiber readings of thousands of hours of removal being done. Although negative air containment systems were in place on those jobs, I had probably 10 concerning readings out of thousands.
Asbestos is like smoking cigarettes in my opinion. One day isn't going to hurt you. Every day for 5 years will hurt you.
Get a professional. Asbestos dust is a real killer, and frankly it's not worth the risk of residual dust - especially if you have young childeren.
In Australia the Queensland government even have a "Dob in a neighbour" program if you think that someone is doing DIY asbestos handeling. That's how serious it is.