Alpha bank is the most inovative bank in Cyprus closely followed by Laiki bank. Although they are a bit slow in terms of security in their internet banking it doesn't mean that their online services aren't first class... Laiki offers SMS alerts tailored to your requirements, so even if a single pound is withdrawn from your account you know about it in seconds with a FREE text message, they have net-loans and net-visas and net-savings account which offer amazing interest rates, a net-current account has an interest rate as good as an offline savings account.
I did a study on laiki banking and found that laiki is commited to making most of it's new customers switch to online and is prepaired to put its money where its mouth is! Alhtough their login methods could be more secure and more "firefox browser compatible" they should do fine if you change your pin number each month.
Trust me, if you had the option of standing in line at your local "Cyta-vodaphone" store to pay a bill or pay for it online in seconds you would not think twice about it!