Data recovery services will charge! For most it will depend on how important the data is compared to what a service will charge. For things you can download again most would say "no way!" For family photos and other unreplaceable things then you have to decide to pay out to see what they can recover for you.
The alternative methods here may cost a blank disk or two when making a comparison to what a service will charge and why most will be a "do it themselfer" and try to recovery things on their own.
As for Recuva that can be a rather limited file recovery program while Windows is up and running while others work when booting live from disk for recoverying entire partitions. Another option not mentioned so far goes a bit further in using another OS entirely which you rescue files from a drive while booting live from a disk or even a usb flash drive. Recover files from Windows hard disk using Puppy Linux | help.artaro.eu
Ubuntu live cd, Knoppix Live on dvd(at one time small and on cd), Linux Mint live, Linux Mint Debiar live, etc. are able to read, write, copy to and copy from MS volumes. For the effort of download and burn to disk or seeing an iso image written to a flash drive made bootable to boot live from you can grab files manually to save to another drive.
The professional services on the other hand are usually sought once a drive has failed completely and can no longer be written to or not even allowing you to see anything let alone copy files from. The serivce will open a drive up under controlled circumstances to read from the platters directly for the fee they charge. You simply provide the blank media or spare drive they recover files to.