Some of the best action movies of the past decade starred Matt Damon as Jason Bourne. Unlike in the past, when charm and wit were what a spy used to navigate treacherous waters, these ultra-modern films focused on the skills and brutality of their main character. In fact, personality and charm were notably absent, since Bourne begins the trilogy with a severe case of amnesia and doesn't even know what kind of person he is -- he just knows that he's a deadly weapon.
Once the series finished, Damon basically swore off returning to the character. However, with such a distinctive look, feel and atmosphere, there was no way movie producers would let the franchise go quietly into the night. That's why it has continued, albeit with a new star (Jeremy Renner) and a new protagonist (Aaron Cross).
In the past, producer Frank Marshall had hinted that Damon might return to team up with Cross, giving movie fans some hope that they'd see Jason Bourne kick some ass once again. However, Damon has basically put that possibility to rest. NME reports that he was recently pretty unequivocal. However, he's also mentioned in the past that he might be tempted back if original director Paul Greengrass was onboard, but that doesn't appear to be happening any time soon.