Most people, if they get talking about their dream game, describe it in terms of other games they already like. As in: it'd be X crossed with Y but IN SPACE!. So I'm asking you, not for your dream game, but specifically which two games you'd cross-breed in order to create an odd new child?
What I like about this question is that you can answer it at whatever scale you like, selecting broad concepts or very specific moments and features. You can say that you'd cross Mirror's Edge with SimCity, taking the big ideas from both to describe a game in which you design the cities you sprint and climb across; or you can be more exact and say that you'd like to combine that one scene in Fort Frolic from BioShock where you smash splicers to music with the procedural and turn-based combat of XCOM. This means that you can probably think of an idea quickly.
If you're doing it with a crowd, it can also be a neat way to find out about games you might not have heard of or considered before, too. You'd like to combine the who-is-the-real-enemy mechanic of Spy Party with an open world game? Watch_Dogs did that, pretty much, with its ability to hack and stalk other players who thought they were alone in their singleplayer game while you pretended to be one of the NPC crowd.
The challenge however is to come up with interesting combinations. I'd love to add Dwarf Fortress's simulation of individual dwarves' moods to a lot of games, for example, but it's not particularly interesting to say that I'd add it to games which are already simulations of lots of little people, such as SimCity. It's marginally more interesting to say I'd add it to Euro Truck Simulator 2, but then I'd need to explain why. Perhaps to populate the world's rest stops with procedural drivers and coffee drinkers who feel forlorn about things? I haven't thought this through.
You don't need to think it through either. Hop to the comments and regale us with descriptions of your own dreamy Frankengames.