There are trips across the bay and to Formentor that go from the port and piers along the coast. Ferries from the commercial port are operated by Balearia and Iscomar - http://www.balearia.net and http://www.iscomar.com
Daily ferries go to Menorca (Ciutadella and Mahon) which take a couple of hours, and there is also a summer ferry to Barcelona. Ibiza? Not that I know of from Alcúdia

thanks for the reply and links,i take it there are ferrys or boat trips from palma to ibiza ?

Yes, Balearia for example does a daily run from Palma, leaves at 8 in the morning and lasts two hours. A later one - at 9.30 - takes four hours. Sorry don't know prices.