In the episode "Tapestry," Picard gets stabbed in the heart. I think that scene is showed a few times on that episode. And in the episode "Cause and Effect" the Enterprise explodes over and over. This means Picard died many times in just these two episodes. It got me to thinking...
How many times does Picard "die" on TNG? In other words, how many occurrences are there where Picard is shown to die or is implied to be dead?
Lonely Among Us - I guess it all depends on how you define "death". Picard is possessed by some sort of energy alien, and beams out of the ship as all energy. He stays that way for over an hour before he manages to separate himself from the entity, Troi senses him, and they beam him back. His body was not in existence for a while, although his consciousness existed - does that count as death?
Time Squared - Picard leaves the ship, the ship is destroyed, and
he's then thrown back in time where he meets the enterprise and is
shot by Picard.
Cause and effect - The Enterprise is destroyed, thrown back in time,
and then it's repeated a few more times before they finally break out
of the cycle.
Tapestry - As you mentioned, Picard's heart gives out and he meets Q in the afterlife. (An eternity with Q is probably his version of hell but I digress).
All Good Things - At the end, two copies of the enterprise blows up
(presumably killing two Picards).
Things I thought about including but decided against it. You can include them if you wish.
Shades of grey - The whole crew should have died from embarrassment, unfortunately the episode ran anyway.
Gambit- Picard is shot by a weapon that is connected to a transporter. Witnesses assume he's been vaporized, and he's declared dead, but at no point is he actually killed - It's just an illusion.
Best of Both worlds - Picard is assimilated and declared lost by Starfleet, but his body is at no point actually dead.
The inner light - in a fake memory, Picard lives out a life as another person. Although mentioned in the comments, we don't actually see him die in the episode. In his fake life he grows old and they launch the probe which would eventually find the real Picard. His 'wife' then comes and explains everything that has happened and he wakes up. Although old, we never see him die. (I just rewatched the scene to make sure my memory was correct).
Remember me - Crusher is trapped in a static warp bubble and everyone else around her slowly disappears. Left off because the 'real' Picard was fine, it was just the version inside Crusher's bubble that vanished.
Frame of mind - towards the end Riker (who is having delusions) is confronted by Picard, Troi, and Crusher. Knowing it's a delusion he shoots himself with a phaser to end the delusion, which causes Picard (and Troi and Crusher) to shatter.