Who's guilty?

I think the brawl and killings were Mercutio's fault, and possibly Romeo's fault for speeding up the process.
When Tybalt asks "What wouldst thou have with me?", Mercutio explicitly answers that he wants to kill Tybalt to end the feud between them, taking one of his nine lives and perhaps more. Mercutio is also the one who first threatens Tybalt, saying something similar to "give me your best shot". In this way he not only provoked Tybalt, but pretty much was asking for his own death. Obviously he was too confident in his own capabilities.
Romeo deserves some of the blame; as he tried to make peace he distracted Mercutio, and enabled Tybalt to slip his knife under Romeo's arm, catching Mercutio off guard. If Romeo had let the affray play out, and not trusted Tybalt to give up fight, either neither would have died due to the appearance of the Prince, or a wound would have been delayed as both would have been brawling at their best.