Its a long long time since I was posted to Akrotiti. Can anyone tell me if you can cross from south to north in a hire car?
Yes you can mate, I went there during my holiday earlier this year. There's 5 crossings now, 1 on foot at Ledra as Penfold said and 4 for cars.
Of the 4 for cars, 2 are to the East of Lefkosia (Nicosia) and 2 to the West. The easterly ones are at Pergamos and Ay Nik, but I did hear a rumour that the 4 Mile Inn at Ay Nik has closed so you wouldn't be able to stage out of there if it's true.
When the wife and me crossed we went North via the crossing just to the west of Lefkosia at Agios Dometios. It was very straightforward, we bought insurance for the North - they had packages that covered you for 1, 3 or 7 days or something like that I seem to remember and had our passports checked and we were on our way. Half an hour after that we were in Kyrenia.
We recrossed to the South via the border point at Zodhia, just to the South of Morfou, it was a nice drive and when you re-enter the Republic you can head West towards Pafos, Polis and the Troodos Mountains or you can head East and you end up back near Lefkosia to pick up the motorway again.
I was out there 91 to 94 and the motorway that was being built has now been completed linking Pafos with Lemesos (Limassol) and out to the east and Agia Napa. We had a Lonely Planet and found it very handy for the holiday.