One example is the Final Fantasy V Four Job Fiesta. This is done every year, often streamed on twitch and played for charities.
I've never actually taken part in it yet, but I have always liked the idea of trying it out. This year's Fiesta is coming up in about 5 or 6 days at the start of June.
There is also the Summer of Old JRPGs over at Kotaku. I haven't taken part in any of these playthroughs at Kotaku, but I have been itching to play some classic (turn-based) JRPGs recently, and this might be pretty cool, depending on how it ends up working.
I think if I was to play along with this and could choose my own list of games to play through, mine would look like this (I would probably have to narrow this down):
Phantasy Star (I own this on the GBA collection)
Final Fantasy Tactics: War of the Lions (I own the PSP version, not the original. One of the best)
Dragon Warrior (don't own this, but I would track down the Game Boy collection)
Final Fantasy (I own this on GBA, but have been wanting to play the PSP version)
Shin Megami Tensei (don't own, but I would try the IOS version)
Chrono Trigger (DS version, in here as it is one of the best RPGs)
Breath of Fire (I own it on GBA)
Golden Sun and Golden Sun: The Lost Age (these are pretty nostalgic for me, I like these games)
Shining Force: Resurrection of the Dark Dragon (I don't know anything about this series unfortunately, I still need to get into it, and this is the only one I own)
Some other cool links:
JRPGs for beginners/newcomers to the genre - Its a community list in the comments
IGN's top 100 RPGs
Shiness - a kickstarter coming to the end of its time period and looks very polished. However, it still has a bit to go before it is funded. So go check that out. For me, I'm done with kickstarter after one of them just took people's money and scammed everyone. The other one I've funded keeps getting pushed back.