yes, but how you do it depends on the make and model.
on my Nokia you go to "contacts" then "options" then "settings". it will show you where your contacts are stored (card or phone) then give you the option to "move all" across. you can also upload onto your pc if you have the software and data cable, then download onto your new phone.
Thanks both -got a Sony Ericsson K660i (for the time being) but its not happening -may have to just go down the route o writing them down,I have read the manual but cant find anything ther will give it another go -its just that I have -as everyone else does loads of numbers and dont want to lose any of them.I dont know whether in the long term its safer to retain to sim or phone??