You can be tried again for the same offence; double jeopardy only applies if you are found "not guilty". It is not uncommon for appeals courts to invalidate a guilty verdict and require a retrial. Similarly a mistrial can result in a new trial at the prosecution's discretion. In addition, some jurisdictions have abolished double jeopardy for crimes like murder (e.g. New South Wales, Australia).
New evidence coming to light can be grounds for appeal - in the case of the Fugitive where there have been no appeals this is one avenue open to Kimble.
Where appeals have been exhausted; this is more problematic. One of the principles of justice is that there should be finality to the verdict. Kimble has gone from presumed innocent to presumed guilty - enough evidence would need to be gathered to demonstrate a clear and unambiguous miscarriage of justice. This may not be within the purview of the judicial branch of government - he may need a pardon from the executive. In real life (as opposed to Hollywood) Dr. Kimble is still in serious trouble.
In some jurisdictions there may be some "innocence" laws that can allow review of convictions outside the appeal process.
Notwithstanding, Dr. Kimble is going away for a long time for "escaping lawful custody" anyway.
