I just released an entire online dating program (which you can hear excerpts from at the link in my signature). I go over this in that program, but I'll give the short version here: I don't even go for the number. After about the 3rd or 4th exchange (by then I usually have them LOLing and asking me a bunch of questions about myself), I ask them if they'd like to meet up for coffee, preferably that day but if not them sometime within the next two days. Girls are on there to DATE, so I always get a yes. That's correct, ALWAYS - I have yet to have a girl turn me down when asking for an on-the-spot or next day coffee date after 3 to 5 messages. From there, I set up the time and place for us to meet, then re-confirm to her ON THE SITE that those are the plans - "Great! So, tomorrow at 6 at the coffee shop on x-street."
Once I've gotten all that out the way... THEN, I ask for their name and number, lol. (Not even kidding - I get the date most of the time before they even know my name...)