This depends on the type of case, and the liklihood of a recovery. Litigation is very time intensive. Unless there is an extremely good chance of a recovery that will result in enough to provide for a reasonable contingent fee, most attorneus will not. The types of cases that lend themselves to contingent fees are personal injury, auto accident, medical malpractice, etc.
Assuming your case arises out of some type of accident, it is a certainty that most every attorney would represent you on a contingent fee basis, as that is the standard for such cases. However, if the issue requiring litigation arises out of another type of situation, you will have to discuss the exact facts and possible recovery with which ever attorney with whom you consult.
There are some cases that can be taken on a contingency fee basis and others that cannot. Under the rules governing attorney conduct, a lawyer cannot take a family related matter on a contingency fee basis. However, as other colleagues have already correctly stated, the rules do allow for personal injury, wrongful death, product liability, maritime accidents, slip and fall, aviation and other injury cases to be handled on a percentage basis. Many commercial disputes may be taken on a contingency fee basis as well. Examples include securities fraud or stock broker deceit cases.
If the case can be taken on a contingency basis, the lawyer will have to fee good about the possiblity of recovery compared to the amount of time involved in the case. Our firm does not consider contingency cases where the prospect of recovery is less than $50,000.
The reason for this is that if you take 1/3 of 50,000 the fee would be around $17K. It is very hard to have anytype of litigation and keep the fees below $15000. Generally as the risk goes up the amount of recovery must also increase.
It is important to remember that there are some areas like criminal law and divorce where FL lawyers are not permitted to do work on a contingency. This does not mean that every issue with divorce cannot be taken on contingency. For example the collection of child support or alimony may be taken on contingency while the original case may not.