Wikipedia says this about registry cleaners: “A registry cleaner is a type of software utility designed for the Microsoft Windows operating system whose purpose is to remove redundant or unwanted items from the Windows registry. However the necessity and usefulness of registry cleaners is a controversial topic, with experts not agreeing on their benefit. The problem is further clouded by the fact that malware and scareware is often being associated with utilities of this type.”
Registry Mechanic is a proper program - there was a review in PCPRO - it is checking for loose registry entries and the like, when software is removed, or updated, and there are orphaned entries cluttering the registry. Quite how much that slows your pc is a moot point, and the aggressive marketing on the net doesn't really give what I would consider an impartial review. I'd leave it alone.
For my money, one of the best tools for speeding your system is defraggler (which is free!). File fragmentation slows a pc far more than odd entries in the registry (which is a very small filing system in comparison). As you load / save files (e.g. a word document), it looks for spare space to store any extra data, and puts a link to that.
A very fragmented drive is like having pages of a book torn out and scattered across your home - the first page says - go to the fridge to find pages 2-4, and when you go and pick up page 4, it says, go to the bedroom for page 5, and so on. To assemble the book to read it - the equivalent of loading a file - takes far more time. A defragmenter puts all the pages together, so it really takes less time.