I met this great girl, and we have been out for a few dates.

Christmas Holidays were coming and she went home to her parents.
We have talked since then on facebook, on the phone for hours.

She gave me a lot of IOI's, for example: calling me funny nicknames, saying to me a lot of sweet and romantic things, asking me to call her and so on. We talked every day for almost a week.

Nothing went wrong, but then she suddenly stopped. I haven't seen her on facebook, and she did not respond to any phone calls. I don't know what could be wrong. Maybe you could say that I did something wrong but I don't think I did, and if so she could just let me know, but no reply since then.

I want to add something more:
After our first date she which was great we talked when we got home, then she suddenly did not reply for a few days and when I could get in touch with her again she said that she was busy with exams, and I thought that she did not like our date, but she assured me that the date was great.

After that we went at a second and third date, we became much more closer to each other, then we kept taking on facebook and phone for almost a week(since she went home for holidays). No sign from her for a few days and that is strange.

What would you advise me to do?

Is she still with her family? That could be it and she's simply busy. That's kinda bullshit she wouldn't even send a text that she's busy though...

Could be another guy... She could also just be nuts. Or you did something that you haven't included here.

What would I advise? Back off and focus your attention on someone else. She'll either come around or she won't... but you'll look like the needy guy if you keep trying, over and over.

Show her you have a life and that she's not the only one competing for you by letting her be anti-social and risking what you've got (which isn't much by the sounds of it - a few dates, that's all... but still warranting at least a call or a text to tell you she's alive IMO).

Thank you for your answer.

I already called her a lot of times and sent her a message that I am worried and so on, but no reply.
I also want to mention that when we were talking the conversation was interrupted by the fact that she used all her minutes with me. Still I think that she should have recharged the minutes on the phone, or at least leave me a message on facebook, but nothing new on her facebook, like I am pretty much sure she did not use facebook this days.

Time will tell what will happen!

Still I am not sure what to do if she comes back saying that she was busy and start apologizing.
Yes she has a lot of qualities that would make her a good girlfriend, but I don't want to live with the fear that she can always disappear, at least she should give me a short message, it wasn't necessary a phone conversation for hours like she did in those days.

OK well if you haven't done anything else you aren't mentioning here... Then you need to read the signs:

She's out, dude.

There's no good scenario here.

1) You keep pestering her and look needy and lose your dignity.

2) You wait for her to want some attention again and then reply to her when she gets back in touch and give her what she wants.

Not exactly wonderful options...

There's a third option though:

3) You're done with her. This is disrespectful and because you're such an in-demand, popular, good looking guy then you're not just going to let that fly... If I were you I'd likely already have pictures on social media of you out having fun, or hanging out with groups of hot girls.

"I already called her a lot of times and sent her a message that I am worried and so on, but no reply. "

I lol'd.