Since it happened so long ago and the conspirators tried to cover their tracks, we are not completely certain who all was involved. There may have been as many as 60 members of the Roman Senate involved.
We are fairly confident that Marcus Junius Brutus (of "Et tu, Brute?" fame, though this quote is apocryphal) was a major conspirator, as well as Gaius Cassius Longinus. We think that Publius Servilius Casca struck the first blow. I've also linked a paper that lists several of the other conspirators for which we have good evidence.
While Cicero was no fan of Caesar, we have no evidence that he was actually involved in the conspiracy to assassinate him. Cicero supported Augustus as Emperor.
While many held the surname Cincinnatus, we have no evidence of any of them being involved in the assassination, and the most famous one, Lucius Quinctius Cincinnatus, had been dead for almost 400 years when Caesar was killed.