Google Checkout competes with Paypal's #2 use case: providing payment processing on third party sites. If you don't need recurring billing and are a US merchant, then it is an acceptable substitute. (I won't say superior, for a variety of reasons -- it is cheaper, free if you use AdWords, but has its own share of headaches.)
Credentials: I sold about $10,000 on each in last 12 months.
Edit: I realize that vaguely saying "It has problems" doesn't help anyone here make decisions. Let me elaborate:
* Google has a Buyer's Remorse feature, which allows a customer to yank back a transaction up to 20 minutes after making it. I don't mind -- I have a 30 day money back guarantee -- but some people probably would. (I also have gotten burned once or twice when people Buyer's Remorse a CD that already got shipped -- I have no convenient way to recall a CD order after it gets sent to the processor's computer. I write that off as a cost of doing business, but it is friction and I hate friction.)
* Google has this "customer friendly" option which it labels as "Opt Out Of Marketing Messages From This Merchant". A more accurate label would be "Hide Your Real Email Address From This Merchant So When You Ask Him For Your Account Details In A Year He Has No Clue Who You Are".
* Google once opted me in to showing a post-transaction upsell (to some sort of environmentalist indulgence -- carbon offset or something) on Earth Day. They included instructions for opting out in an email they sent me, which I did immediately. I wrote a letter On Dead Tree (TM) to express how strongly I feel that they should not make their political statements during the middle of business transactions which I am paying them for. (Any customer who mistakenly clicked the button would find it nearly impossible to navigate back to the software they just paid me for. Guess whose problem that is? Guess who they think is trying to be a pushy git and sell them a carbon offset totally unrelated to my actual product?) If Google wants to interrupt someone's browsing experience to offset a carbon offset, I hear they have some web traffic of their own who they can bother.
* Ironically, their search interface sucks. (Can't search for a customer by name. I kid you not.)