What is the standard fee charged by most lawyers that practice and provide legal services to persons that sustain a personal bodily injury as the direct result of the intentional, negligent, reckless or careless actions of another?

In the large majority of cases, at least in the US, attorneys that specialize in the field of personal injury are willing to take on the case under contingency. With a contingency fee agreement, which must be in writing to be valid, this means that the attorney will only receive a fee of +/- 33.3% of the net recovery, with the lawyer also agreeing that he/she will not be paid anything (i.e. a fee for her legal services rendered) unless the attorney is able to recover a monetary settlement, verdict or judgment for you, the client.