I'm thinking about Shenmue again. The appeals for Shenmue 3 never seem to die, and Sega has admitted its their #1 requested sequel from fans.
I think asking directly for Shenmue 3 is a mistake. There hasn't been a brand new Shenmue release since Shenmue II seven or eight years ago (depending on whether you consider the 2001 Dreamcast release or the 2002 Xbox version the definitive release). Given the tremendous costs of action/adventure games of this quality (lots of locations means lots of art, lots of characters to model, lots of voice work), it's a bit much to expect Sega to jump right in with an expensive-to-produce sequel to an older game, fan favourite or no.
However... re-releasing the first Shenmue as a downloadable game on XBL and PSN, that's a different story. Shenmue's structure allows you to either release the entire game as a single downloadable game, or to release it episodically, given Shenmue was designed as an episodic game, and each retail release contained multiple chapters of the game.
Unlike re-releasing games for older consoles, Dreamcast games are quite competitive visually and audially with downloadable games for the 360 and PS3, so nothing in the way of new art or audio assets should be required. Obviously an engine would be required, either to emulate the game or one built to use the game's assets (the latter being preferrable). When you have tens of thousands of people viewing YouTube appeals for a Shenmue 3, that suggests a strong enough fan-base to do a profitable re-release, and Dreamcast code is considered easier to work with than some older systems (Saturn, Jaguar, etc.). Some of the knocks against Shenmue (load times, disc swapping) would be solved by digital distribution. And considering the amount of duplication on the Shenmue discs (commonly-used assets were repeated on every disc to reduce the amount of swapping), the file size could be made less than the sum of its parts.
I think Shenmue's an interesting case. Not only did it have a rabid fan base on the DC, one that has remained surprisingly loyal to it almost a decade later, but it was also held up as the standard bearer for the DC against the PS2 by many fans. I think there are some PS2 fans out there, because of this, who have never tried it and would be curious to do so.
Failing all this, with absolutely no programming required, Sega could release Shenmue: The Movie (whether for free as a promotional effort, or for a reasonable number of Microsoft Points) on Xbox Live, and then work with Microsoft to distribute the Xbox version of Shenmue II (which is fully backwards compatible) via the Xbox Originals section of Games On Demand. If they chose to test the waters that way, they may be surprised.
A campaign to get Sega to do any of the above is more likely to be successful than a campaign to get them do Shenmue 3, I would argue.