On our old WoW guild application form we included:
"Please rank all of the Star Trek captains you know from best to worst"
and then gave them a nice big empty text box to go to town in. Some answered seriously, and exhaustively. Some only knew Kirk, or didn't know any at all. Some chose to go off on a rant about Star Wars being better, or include a joke or tell an anecdote about their relationship to scifi.
Whatever the answer we always learned something about the person and that was a good jumping off point if they got accepted. We did get the occasional humourless "wtf this is stupid" type response but, shockingly, this was rarely the only reason we had for denying such applications.
My usual go-to is to ask what their latest/current obsession is. It works really well for a few reasons:
it's nice and simple to ask - it doesn't require a monologue/wall of text to set up, and it doesn't require you to know anything about them to ask it;
it's both as personal and as low-stakes as they want it to be. They can give very intimate, in-depth answers if they feel like it, or they can just mention something like the latest film they enjoyed. There's no risk of making them uncomfortable by asking it;
it lets you filter out boring people who don't really take interest in anything;
assuming they do have interests, it often gives you plenty of opportunities to dive into deeper conversation;
it's often engaging for them because they get to talk about something they're passionate about;
it's often interesting for you because people talking about things they're passionate about is awesome (and often attractive).
it's pretty much always relevant and fresh because their latest obsession will change over time. This makes it particularly great for things like dating sites/apps because people's bios will often be out of date and/or they'll have talked about the things mentioned in their bio so much that they're kind of sick of them.
I've actually had multiple people on dating sites tell me how great a question they think it is, and that they're going to use it themselves in the future. So obviously it's not just me who thinks it's a great question!
Something that'll lead to fairly flippant, casual, low-stakes chit chat about completely unimportant bullshit. People like getting a chance to get a sort of baseline reading of you, so talk about flippant, dumb, unimportant things for a little bit. Preferably ones that they are 100% certain to have recently experienced themselves, so it can go back and forth smoothly.
Given the diversity of humanity, this is a fairly short list. Weather, food, free time hobbies, etc. If they're like a student, or work in a particular industry, that opens up a lot of options. But for a stranger? Just got a few to pick from. So, just pick one.
They call it "small talk" for a reason though. The real purpose of the talk has absolutely nothing to do with the actual subject of the discussion.
So what do you like to do for fun? Or, What are some of your hobbies?
I find these much better than "so what do you do for work?", which is what I'm asked constantly. "Yes, person who I don't know, let me discuss work during my free time with you."
How many hard boiled eggs do you think you can fit in your mouth?
If they are an acquaintance from work or someone I see frequently it might make them laugh and if they give it a moment of thought they're probably the kind of person I'd enjoy talking with.
In all seriousness though someone already said asking what they are obsessed or passionate about at the moment and I'd probably go that direction. It's nice to see people enthusiastic about stuff they really like especially if they don't normally get a chance to talk about it.
Around this time of year one of my best conversation starters is "What's your least favorite Christmas song?". Everyone (at least here in the US) has at least one Christmas song that annoys the shit out of them, but you'll get tons of different answers.
One person closes their eyes until the other person/people decide on a number 1-10.
After they all agree, the person opens their eyes then asks the group to rate an item from a category 1-10. Do this with 3 different categories. At the end, the person tries to guess which number was agreed on.
So, the group could agree on 7/10 and the guesser could ask "types of beers" and the group could say lagunitas, skulpin, etc ...
Other good questions involve "people we both know", "sexual experiences"...
Just had beers with my wife and a complete stranger. She was nice, but I was not in an n overly talkative mood.
Just asked her about herself regularly, and happily listened to her talk about herself.
Turns out she's quite interesting. We both agreed we'd like to meet her for beers again.
But. Where you from? How'd you end up living here? Family nearby? Miss them? See them often? Your dad does WHAT for a living? We had a similar pet, does yours do X? Think you'll stay here, or considering another area to live? So you're not getting on well with your sister? I can understand that, what else have you tried?
Etc etc etc. All about them, but can be genuinely interesting.