I have an iPhone and any app or music/tv/film purchase I make via iTunes I do from my phone. The only time I connect to iTunes on the laptop is to sync my device.

Apart from syncing my phone with iTunes (wireless sync doesn't work with our ancient laptop) is there any other reason why I need to use iTunes on the laptop/PC?

...and I only sync in case I lose my phone and need to set up a new phone.

Not since iOS 5, no.

That's what I thought. Now if I could just get wireless sync to work I'd be sorted and I'd never need to use a computer at home again.

You only really need to sync to iTunes if your adding your own ripped CD's to your phone.
As long as you've setup iCloud then the phone will automatically backup during charging if it's locked and there's a WiFi connection. (it doesn't backup your ripped music though)

except you would still need a computer at home (and in use), otherwise wireless sync wouldn't work.

you still need itunes open and running for itunes wifi sync to work.