When this topic from Long and Short Reviews came up, I had to think about it. I was trying to avoid the usual ones I come up with for these things, like Jane Eyre or Emma Woodhouse, who I would certainly like to meet but who tend to be the type of characters everyone thinks of.
Although it would be interesting to meet Emma Woodhouse and see if she's as charismatic in person as she seems to be in the book, given that everyone likes her in spite of her attitude.
But the one I ended up deciding on? Lux Lisbon from "The Virgin Suicides". Lux is the character most clearly described and has the most life on the page - she's lively, she's fun and you want her to get what she wants. Which, as any new reader can probably tell from the book title, isn't going to happen, but despite knowing she's walking towards a tragic end, we want her to win.
So which characters would you want to meet?