You'll never stop people being able to steal the games from you, but you can take steps to ensure that the likelihood of this happening is greatly reduced.
A very thorough set of T&Cs, drawn up with the aid of a solicitor, would be the first place to start. However, you might find it tricky to enforce this 'contract' to anyone under the age of 18, so that might pose some problems for your fledgling rental business.
You've then got to find some way of verifiying the identity of your customers so you A) know who you're dealing with and B) know where to send the debt collectors when they decide not to return the stuff they've rented. As you'll probably be restricted to people over the age of 18, I'd ask for some form of photographic ID with their address on (i.e. a photocard driving licence) or a passport and a utility bill, etc.
And lastly, you'll probably need to keep their payment card details on file (there are various issues surrounding this that the solicitor will be able to advise you on) or find some other way of ensuring you can easily 'collect' any late fees, fines, etc.
Ultimately you've got to remember that someone will screw you over at some point, so don't forget to build that into your business model when you're drawing it up. But as long as you can 'afford' to lose the odd thing here and there (and waste time trying to track the buggers down) you'll be okay.