Authorities say seven people were injured on the ground, and they don't believe terrorism was involved. Fire Battalion Chief Bob Franco said the pilot's remains were found in the area of the plane wreckage.
The crash frightened Los Angeles residents and tourists who watched the plane sputter over the city before taking a nose-dive into the building. The plane plunged through the two floors of apartment units to the ground-floor garage.
"All of a sudden, I heard a real loud swirling noise ... then a real loud bang and the whole apartment shook," said Will Binder, who lives in an adjacent apartment building.
"We heard the plane going around in circles and it started losing power ... It hit. We saw black smoke," said Carlos Mancilla, 43, who was shopping with friends on Melrose Avenue when the plane crashed.
Three of the seven injured were taken to Cedars-Sinai Medical Center. They included a man who was burned over 25 percent of his body, Fire Chief William Bamattre said.
The building, which had 14 units, burned fiercely at first, but firefighters had the blaze under control in about a half-hour. By then about half the building was gutted.
The plane was believed to be a four-seat aircraft that took off from Santa Monica Airport about 10 miles away, said Federal Aviation Administration spokesman Donn Walker.
A single-engine Bonanza BE-35 departed Santa Monica at 3:45 p.m. Seven minutes later the Santa Monica tower gave its pilot a frequency change to contact a radar control facility for flight guidance. Walker said they never made contact with the facility.
The Bonanza pilot did not file a flight plan and was operating on visual flight rules, he said. He did not have any other information about that plane, including how many people were aboard.
Adam Krolfifer of High Point, N.C., was in line waiting to see a taping of "The Late Late Show with Craig Kilborn" when he heard a plane overhead.
"We were waiting at CBS Studios. I heard a plane, like he was doing acrobatic moves. About four minutes later, we saw a huge plume of black smoke," said Krolfifer, who was in Los Angeles on vacation.
"It sounded like it was making maneuvers, the engine getting stressed out," he said.
Mancilla and his friends ran to the building after the plane hit and saw a man on the second floor getting ready to jump, he said.
"We were telling him not to jump, but he said, 'I'm jumping,"' Mancilla said.
As he jumped or fell, "there was a second explosion and we were covered with smoke," he said. The jumper was apparently not seriously injured.
California authorities notified the Homeland Security Department about the crash, and the agency was working with state and local officials to monitor the situation, spokeswoman Rachael Sunbarger said.
FBI agents were sent to the crash site but only as a precaution, FBI spokeswoman Cheryl Mimura said.
"There is no indication that it is an act of terrorism," Mimura said.