The problem is that to give money over the internet requires a debit or credit card payment and the processor gets charged for this - typically 2.5%, so you are not going to get it free.
PayPal is as good as any for this. The alternative is for one to make their bank details available for donors to deposit monies by direct bank transfer. This is free, but can take a few days to go through, and there is nothing to stop the nominated person from running off with all or some of the money.