A few days ago, Google unveiled Checkout -- their e-commerce tool for making purchases directly through Google. The service is straight forward: a little shopping cart appears next to your AdWords text advertisements. Someone clicks on the shopping cart, pays you through Google's site, and you ship it. Pretty simple. You can also add their payment services to your website, so that people who have a Google Checkout account can buy products from your site a with a couple of clicks.
This is similar to PayPal in that it's a trusted third party mechanism for making payments. Both of them support online payments for goods and services, but they're pointed in different directions: PayPal is geared towards people sending each other money; Google Checkout is designed specifically for e-commerce. PayPal's primary commercial use is within eBay's web site; Google Checkout is distributed everywhere AdWords are shown. PayPal operates independently of advertising efforts; Google Checkout is (currently) strictly tied to AdWords.
PayPal and Google Checkout overlap, and there will certainly be fierce competition over common ground, but I think they're sufficiently different (and well funded) to survive in their own right.
The logical extension of Google Checkout is through Froogle, their shopping comparison search engine. With Google Checkout handling financial transactions, and Google Base providing a huge inventory of products, the mating of the two is a natural progression ... and if that happens, who's going to feel the heat?
For the last several years, Amazon has been making a huge push to become an end-all, be-all market place. Their core business may be books, but their partnership with other retailers and heavy promotion of sell through merchants has expanded their business tremendously. Froogle + Checkout directly competes for those customers, and with Froogle and AdWords results along side Google searches, I think it would catch on very quickly.
My expectation is that Google Checkout + AdWords is the testing ground for the technology before combining Google Checkout with Froogle. If that's the case, we'll probably see little green shopping carts on Froogle and at the top of our Google searches before the winter shopping season.