I live in the Florida keys, and I have some unpaid medical bills which have been sent to a collection agency. Can my wages be garnished? And also, can they take money from my bank accounts? My medical insurance covered the great majority of the bills.

If they sue you and get a judgment, then they can garnish your wages.

They will have to sue you in court and receive a judgement, once they do that, yes they can. Of course if you have money in the bank, why not pay or start a payment plan.