Well ok - I thought this topic was meant to be more around actual game ideas (which at least are a little bit fleshed out in terms of the general vision of the game) and not just one big collection for inspirations...

Considering the "unique mechanic": I think while it isn't necessary to have one it helps. I think everyone enjoys a new gameplay mechanic if it's fun. It's nowhere a must have in order to produce a good game but I think people enjoy playing something new and fresh plus it makes your game stand out. I guess especially the latter is important when aiming for the mobile market where you nowadays have these huge appstore with literally thousands of games and applications. As I see it even great games tend to disappear in the great flood of new games and so I think it's extremely useful if your game has a little bit more to offer than "Everything you've already seen elsewhere just with very well done execution."...

What shouldn't be done in my opinion is to focus too much on this one unique feature / mechanic. Under this perspective I tend do agree, that you don't need this in order to create a good game so an extreme focus on that one thing probably will turn out counterproductive...