We recently had a session where one player didn't show up for an Edge of the Empire game, and the previous session had ended on an important scene right before a combat encounter. So the GM surprised us by showing up, tossing some gum on the table, and announcing that we'd be playing a quick one-shot of a game called All Outta Bubblegum (a quick search couldn't locate the rules, but follow the link to a relevant blog post). This turned out to only last about an hour and a half, leaving us time to test out another simple game I'd been interested in, Lasers and Feelings.
Both of these are extremely simple RPG systems less than a page in length. Both have a binary mechanic where you roll a single die and in certain situations you want to roll over a certain number, whereas in others you want to roll under. In All Outta Bubblegum that number changes over the course of the session creating an interesting pacing mechanism. In Lasers and Feelings it stays the same, defining your main "stat."
All Outta Bubblegum starts you with 8 pieces of gum and you roll under (on a d10) to do something mundane, roll over to do something kickass. You can spend a piece of gum for an autosuccess. Once you're out of gum you can only succeed at kickass tasks. Check out the blog post linked above for the nuance this provides. We didn't really see that in play, but we did emphasize the resource-management aspect of it, and the game did tend toward an arc that made it easier and easier to be kickass. There was an interesting meta-game wherein you try to make sure you have some pieces of gum left at the end just in case, but you still want it to be relatively easy to kickass. It creates a tension unique to this system, and it was an interesting change of pace. If you're intrigued, I'd suggest playing it as a beer-and-pretzels game. Yeah, I know I didn't link the rules, but based on my experience that blog post is really all you need to play. There's also an episode of the One Shot Podcast (episodes 20-21) that inspired my GM to choose this system (I also listen to this podcast, but I haven't personally listened to that episode).
Lasers and Feelings has one mechanical stat for each PC, which is their number. The number ranges from 2-5, with 2 being slanted heavily towards "Feelings" and 5 being slanted heavily towards "Lasers." 3 and 4 are for more balanced PCs. Basically, if an action falls under the broad category of Feelings then you want to roll over your number on a d6. If Lasers is more appropriate to the action, you want to roll under your number. You can get more dice by being prepared, being an expert, or having someone assist you. If your exact number is rolled then you have Laser-Feelings, which doesn't count as a success but does allow you to ask a question about the situation to gain some more insight. Since you'll often be rolling multiple dice you can also get multiple successes (1 success has complications, 2 is great, and 3 is a critical success). For our session we played a Futurama game, where I played Professor Farnsworth (number 5), and the other two PCs were Dr. Zoidberg (number 3) and Fry (number 2). The system supported that setting thematically, and resulted in a lot of slapstick, ridiculous humor. We ended up shrinking Fry down to enter the bottom end of Kiff's digestive tract where he battled worms who were trying to mind control Kiff into destroying the Professor's latest doomsday device, destroying the quantum tunnel in the process.
Whereas All Outta Bubblegum's core mechanic created an interesting pacing and resource management meta-game, Lasers and Feelings offers a really simple but surprisingly flexible party-game that self-generates character development, more strongly emphasizing the "roll-playing" part of a Roll Playing Game. All in all, both were interesting experiences.
In the back of my mind I'm often thinking about what would be a good RPG to play while backpacking (I have yet to actually play an RPG while backpacking, but it's still something I'd like to have in my back pocket). Either of these would make strong candidates, and seem far more practical than any other alternative I've thought of so far. Especially Lasers and Feelings, considering those mini D6s that are pretty easy to find, and weigh almost nothing...