I want my site to accept bitcoins (and automatically reward users with it), but do not want to deal with the security issues that would entail.
Is there a SaaS (Software as a Service) which could handle all the hassle for me?
Coinapult has an API that you can use to send coins to a user's mobile SMS/text number or via e-mail.
It's not really the right way to do it but it is one way of doing it.
You could also do it by distributing an Instawallet URL. The person that knows the Instawallet URL can spend the funds.
Redeemable codes would be another method. You can hand out Mt. Gox redeemable codes denominated in BTCs. The user needs to create a Mt. Gox account to redeem the voucher though.
You could also distribute a private key like what is done for Paper bitcoin wallets. The methods for redeeming those are not user friendly though.