Word on the street (via waxy) is that Google is set to release a PayPal competitor called Google Wallet. A thread at Techdirt notes that Yahoo!, Microsoft, and eBay have all tried to launch similar services that met with little or no success in the face of competition with PayPal.
I doubt Google is focused on competing with PayPal, at least in the short term. This move, if true, makes a lot of sense for Google. They already have an internal payment system set up to collect and distribute AdSense revenues, a store selling t-shirts, bean bags, search hardware, they sell software, and they've indicated that with Google Video, people will be able to charge others to view videos uploaded to Google's servers (with Google taking a small cut). Taking the core of that internal payment system, it would probably be technologically trivial** for them to open it up for anyone to pay money to anyone else (instead of just individual --> Google or Google --> individual). The line above about their Google Video plans -- "people will be able to charge others to view videos uploaded to Google's servers (with Google taking a small cut)" -- already sounds a lot like what PayPal does. This is the Andre Torrez school of product development...build something that solves a problem you're having and it'll probably be useful to a bunch of other people if you let them use it too.
Plus it leverages their existing user base. If you've already got an AdSense account or are going to charge for your video through Google Video, you're already a GWallet user...and signing people up through their GMail/Orkut/Blogger accounts would probably be pretty easy as well. This move may also indicate that Google is planning to charge a wider range of people for products/services -- maybe a "pro" version of Gmail, a robust, commercial API to their search results, or even a music store? GWallet would be needed infrastructure for ramping up from paying relatively few AdSense users to (potentially) anyone who uses Google. It makes sense for them beyond trying to gain a foothold in the online payments space.
** Getting the banking stuff sorted out is another story though...but as PayPal has shown, if you can get that set up, there's plenty of revenue to be had.