Lots of good answers already. Do remember that not all invisible thread is created equal. I like SewArt Int. (nylon) because it has a matte finish. Superior's Monopoly is great and the Sulky Polyester invisible is also pretty good. Haven't used YLI or the others, and avoid the stuff that feels like fishing line. <G>
Do be careful when you use nylon invisible. It doesn't stand up as well to heat. Story: I used to work as an alterations tailor in a major department store. We used an industrial blind hem machine and gigantic cones of nylon invisible thread to hem pants.
Someone came in and needed the hems put back in their pants because the thread "disappeared" in the dryer. <G>
So it can happen if you aren't careful.
But I do love using invisible to quilt with for all the reasons given.
Have fun,
Pati, in Phx