transfer old data to new phone

Hi Guys, Sorry I am new to this techy stuff.
My six month old Desire has taken to switching itself off and on at random. I am getting a new one but how do I transfer downloaded applications from old to new phone-----( assuming I can get it to stay on long enough !!!). If I have a game with score records can this be transferred??
I have backed up data but I don`t think the applications are transferred to the sdcard.would be grateful for your assistance.
A

 

Thanks xyro.
I managed to download it and then my phone reverted to its on-off routine. Grrrr. will keep trying.
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I tried Mybackup a suggested but I have lost everything I wanted to keep as the program will not work on the new phone.........unless I buy the pro version....talk about being held to ransom.