"Time Squared""Time Squared": Picard shoots and kills another Picard. (Not a hologram or clone and not an imagined death, but an identical Picard who was from a slightly different moment in time.)
"Samaritan Snare""Samaritan Snare": Although not terribly explicit, some of the dialogue suggests that Picard may have been briefly, clinically dead on the operating table (he had no metabolic processes at one point). Ultimately, he was saved by Pulaski.
"Cause and Effect""Cause and Effect": Everyone on board dies (then it gets undone in a time loop).
"Tapestry""Tapestry": He dies on the operating table, and then comes back, possibly due to intenvention from Q.
"Chain of Command""Chain of Command": Presumed dead after being captured by the Cardassians.
"Parallels""Parallels": Picard is dead in various alternate timelines. The deaths are not shown on-screen, but that seems to be okay by the guidelines of the question. Also by the guidelines, this gets counted as one death (no matter how many timelines he dies in).
"Gambit""Gambit": Picard is declared dead after he is "killed" by a transporter weapon.
"All Good Things""All Good Things": Two Enterprises blow up, presumably ending two Picards. Will count these as one death.
GenerationsGenerations : Picard looks to have died on Veridian III (due to explosion of the Veridian star) just as Kirk seemed to have died aboard the Enterprise-B. In actuality, Picard was saved by the Nexus (just as Kirk was), and we find this out a few moments later.
"Azati Prime""Azati Prime": This is an Enterprise episode that takes place partly in the 26th Century. By this time, Picard would surely be dead. (I'm only including this one because of the "Living Witness" example in the Janeway answer, even though it means that Janeway's count should increase by 1 too, as a result.)
"Lonely Among Us""Lonely Among Us": Picard exists for a period of time only as some sort of energy field out in space. He eventually gets saved by the power of terrible sci-fi. I want to file this under "temporary death", even though his consciousness still seemed to exist...somewhere out there. Also discussed here.
"The Best of Both Worlds""The Best of Both Worlds": Picard is declared a "casualty of war" by Admiral Hanson. He was not dead, but considered good as dead.
"The Inner Light""The Inner Light": Picard's alternate probe-based persona presumably dies, outside of the simulation. But we'll never know for sure.
"Remember Me""Remember Me": Crusher is trapped in a static warp bubble and everyone else around her slowly disappears. Picard is one of the last to cease existing before we really know what is going on. It's true that Crusher has a hunch about what is going on before Picard disappears, but we (the viewers) don't know that she is right yet.
"Frame of Mind""Frame of Mind": Riker shoots himself and "shatters" his imagined Picard in the process.