In a sense, roleplaying games are all about giving the PCs choices and letting them make them. Most of the time this is just part and parcel of the routine of buying equipment, choosing spells, and figuring out which dungeon to raid for loot.

Sometimes the GM offers a choice that feels like A Choice. Then you know some Real Roleplaying is about to happen.

Even better is when it can come from the mouth of a fellow PC.

Transcript

GM: ... So, to summarise: No, you don't have a jetpack, R2 units can't jump, and you can't climb that flowering shrub. But just to cut this short: you can get up on tiptoes.
R2-D2: I don't have toes.
Luke: Are you trying to make this difficult?
R2-D2: It wouldn't be fun if it was easy!
Yoda: Why do you keep looking outside? Brunhilde, do you see?
Luke: {sotto voce} Note to self: don't ask about Brunhilde.
Yoda: Time for dinner! Two choices, you have. Choice number one, the bottle!
Luke: That's blue milk! I've been looking for that everywhere!
Yoda: Choice number two, the cauldron!
Luke: That didn't sound appetising at all...
Yoda: You can take the blue milk, and become like everyone else.
Yoda: No more Force, no more danger, no more... expectations.
Yoda: Or, take the red brew you can!
Yoda: Flush out the last remnants of the blue milk from your past, it will. Realise your full Jedi powers.
Luke: Why do I keep getting offered these binary choices?