Depends on the context, but generally yes, people like to talk about themselves, and it's a good idea in most cases to give them the opportunity to do so.
At the same time, you don't want to turn a date or an interaction into an interrogation.
If a girl is shy or reserved and you keep on firing off questions she'll feel like she's in an interview, and unless you can find a more creative way to build rapport, she's not going to be too comfortable fielding question after question from a stranger she just met (unless of course she's already super into you).
Of course being a good conversationalist includes being able to ask good questions and being a good listener, but it also involves being able to adapt to any given context.
Going in with the mindset of "I'll ask open-ended questions, listen, and re-direct the conversation back to her when she asks about me" is great until you discover she's shy and too reserved to answer at length or she can't hold a conversation. It's great until you discover her interest is medium at best or that she is using the same strategy as you and you end up playing question hot potato with each other.
Overall, I do think asking open-ended questions and listening are great tools to have in the conversationalist skillset (active listening might be the most effective out of anything else).
However, a well-rounded schmoozer, in addition to listening and open-ended questions, will know when to invite the right amounts of humour, wit, charm, intrigue, and even vulnerability into a conversation.
