I watched both Bourne Identity and Bourne Supremacy on DVD before seeing this in the theater. I'd been waiting for this since before they started filming. I wasn't disappointed.
Minor spoilers below-
Overall it was good, but it also lacked the continuity of the first two. Identity and Supremacy both flowed gracefully between adrenaline rush action to introspective drama. This movie felt choppy at times. The plot-building down-times were slightly too drawn out. That caused the following action to feel too frenetic.
Camera: Speaking of frenetic, the trademark Greengrass shaky cam was present and very annoying to me. I know its has been talked/whined about to nausea on the message board, but it doesn't mean it's not relevant. All the martial arts training the actors went through was totally wasted. The ridiculous camera cuts and wiggling camera ruined most of the fighting in the movie. It is a cheap, student director trick to make the film feel unsettled. I'd expect those techniques to be used in some horror flick made for high school kids, but not in this classy, adult, action series. Too much extreme close-up also. Do some framing. Get some interesting shots. Constant close-up feels like lazy directing to me.
Story: The story was VERY confusing at first. They thrust new names and faces upon you from the get go. Gave me the feeling that you get when you come into a movie late and know you've missed some crucial information. Felt rushed or compressed for time reasons. After you catch up however the story is quite good. It's enjoyable following leads along with Bourne. HOWEVER, I did NOT care for the whole last scene of Supremacy (Landy/Bourne on the phone) being in the middle of Ultimatum thing. It basically makes the movie a half-prequel. I thought that was awkward.
Cast/Characters: The star of the movie is the action. Obviously there are only two originals left. Bourne and Nicky Parsons. Them teaming up was kind of odd to me. I think they just wanted to give Bourne someone to protect to and confide in. Unless I completely missed something, they never even tell you why they teamed up. The other assassins in the movie were pretty quiet. This felt like Gilroy/Greengrass/whoever wanting to not leave open ends. Understandable but disappointing. Seriously, Damon with Clive Owen in Identity and Marton Csokas in Supremacy.. Those scenes were phenomenal. These assassins are as uninteresting as Castel (the first fella Bourne fights in Identity). The cast in general has degraded as the the series went on. Clive Owen was practically an afterthought. That's a measure of strength for that first cast. The second, they basically trade Chris Cooper for Joan Allen.... Not exactly equal. This one trades Brian Cox and Franka Potente for 3 actors to be named later. Nothing against David Strathairn, Scott Glenn, or Albert Finney, but they're not the first names that come to mind for this kind of series. Aside from a couple pauses that seemed to long, the acting was right on.
As a whole, it was successful. Felt like they wanted to get the series over with though. If they would have trimmed or rearranged the slower parts, eliminated Scott Glenn's part entirely, zoomed out, and taken the camera away from the seizure victim, it would have been perfect.
ENDING SPOILER
I don't see why they leave Bourne alive at the end. It was my understanding this was the conclusion. They clearly made reference to the very beginning of the series with his silhouette floating motionless. I thought that was going to be it. A full circle type of ending. I did like Nicky reacting to the news report though.
SPOILER SPECIFICS WARNING - QUOTE FROM MOVIE BELOW -
Bourne's last line at the end "Look at this.. Look at what they make you give." quoting the first assassin he killed, I loved that. The final scene was great. (Except that it was Vosen {Strathairn} that shot at Bourne. Why would he do that? Just out for vengeance? If he was angry enough to murder, why not shoot Pamela Landy after she faxes his top secret file? That didn't make sense.)

This movie is pretty awful but I have some interesting information about it:
It was filmed in 1976 at Northern Arizona University in Flagstaff, AZ, as well as at Oak Creek Canyon near Sedona, AZ. A good bulk of the extras in the film are then-drama students from NAU. I was a freshman there that year, minoring in theatre, but for some reason I didn't get involved with the production. I did however know several people who did and can supply this rather odd fact:
There is a scene in this movie where two of the principals, as part of their hazing ritual, have to run naked into the woods. They are seen from behind in the movie, doing just that. The thing is, those aren't the actors at all but two guys I knew from the theatre department. The identity of these "stunt posteriors" will remain anonymous, at least to this website, unless they decide to, um, "reveal" themselves!