A Quick Summary
So you wan to know what happened to Ultimate Spider-Man. Well it's a pretty tragic story filled with emotion, but first you need to understand what the Ultimate Universe was (I say "was" because of a recent even known as Secret Wars).
The Ultimate Spider-Man comics were created back in 2000 with Brian Michael Bendis as the writer. It was part of a greater series of comics known as the Ultimate Comics, which made up the Ultimate Universe; however the Ultimate Spider-Man comics were the most popular out of all of them. The comics provide slight spins on Spider-Man's origin, his villains, his friends, etc.
The Nutshell Version of the Comic
So let's skip all the way ahead to his death. It begins with Norman Osborn breaking out of prison along with many of Spider-Man's foes (Sandman, Electro, Doctor Octopus, Kraven, etc). Many of these villains agree to kill Spider-Man...no surprise. However, Doctor Octopus doesn't agree and Norman Osborn kills him in a fit of rage.
The group of super villains head over to the home of Peter Parker to hill him (Norman Osborn has known Spider-Man's identity for a long time and told the other villains). Peter Parker finds out about the breakout and swings over to try to stop them. On his way, he sees an explosion on a bridge, which was a different superhero conflict (honestly, I don't know much about it). As he swings over he notices the Punisher aiming his sniper rifle at Captain America, and Spider-Man (being the hero that he is) puts himself in the way of the bullet and it pierces cleanly though his side.
He woke up with no one around to help him. He webbed up his wounds and swung over to his house. While he was doing this, the group of villains were already at Peter's home where they encountered the Human Torch and Iceman (who were staying with Peter's family). They all fought, but the villains came out victorious. Spider-Man arrived moments later unmasked and fought the group of villains one by one with the entire neighborhood watching.
Eventually Norman Osborn is the final villain left and he and Spider-Man have a final face-off that ends with Spider-Man bashing Norman Osborn several times with a large truck until he's dead (which let's be honest, he really isn't).
The final moments of Peter Parker are spent with him laying in his Aunt May's arms with his friends and his girlfriend Mary Jane next to him. He tells his aunt that it's ok that he's dying because even though he wasn't able to save Uncle Ben, he was able to save Aunt May. His final words are him telling Aunt May that he did it as his voice trails off.
My Personal Opinion on the Matter
Honestly I absolutely love this comic as it provides a good death for a superhero. If one's favorite superhero is going to be killed off in the comics, then the superhero better be killed off doing something heroic (not like the death of Amazing Spider-Man back in late 2012).
I also enjoyed that they brought back Mark Bagley, who was the original artist for the Ultimate Spider-Man comics before he put down his pencil on the project after many, many issues. His art is absolutely fantastic and I love it when a comic book series keeps the same artist. For some reason it seems to keep the atmosphere of every issue the same as opposed to certain characters looking different from issue to issue.
It also opened up the running for a new Spider-Man a.k.a. Miles Morales (an article for another day).
If you are interested, check out this fan video made revolving around the death of Ultimate Spider-Man. It's incredibly well done and the editing is absolutely beautiful.