I am currently on an H1B to expire in 2012. If I quit how long do I have legally in this country? Finding a new H1B is impossible. What are my other options to remain in the USA legally...besides finding another H1B?
You have about 30 days or less to apply for a change of status. The list of temporary visa types range from "A" to "U'. Look at the list, and ask your question again.
Technically, you are out of status as soon as you stop working for the petitioning H-1B employer. There is a memo that says if you leave within ten days of this you aren't really in any trouble, but this has nothing to do with applying to change status here.
Historically, USCIS would accept pay statements/stubs issued in the last 30 days before a filing as evidence that a person has maintained H-1B status for purposes of granting a new H-1b or other visa here. they have become more difficult about this, however. - you really need pay stubs right up to the date of filing these days.
Other possibilities: you can enroll in an academic program, get an I-20 form from a school, and apply to change status to F-1 Student.
You can decide to remain as a visitor for a while, and file to change status to B-1/B-2 Visitor.
You might be eligible for one or two other possibilities, but it would require a review of your background to determine this. Speak with a lawyer directly.