I used GC for I think 4 years. I never saw its use exceed 1% but it was solidly #3 behind credit card and Paypal. Then again, after those 3, how many other payment systems can people name?
So why did we drop it? First, it's convoluted. People leave your site and never return. Google sends you a series of XML callbacks when someone pays. They have really good documentation, tho (second only to Paypal, IMO). Debugging is screwy because it's all callbacks as well.
Second, GC has no phone support. Support is only available via email or their forum and it's not easy to come by. We had an odd circumstance where someone filed a chargeback and Google granted it (more on that in a sec). We contacted the customer and they reversed the charges but the money got "stuck". GC considered the case closed and yet Google had our money. Took 4 months to get resolved (a lot of work for not a lot of money). By contrast, I can call Paypal 24/7 with issues.
Third, you play by Google's rules or else. GC mandates you ship all items over $250 with signature confirmation. If you don't, the customer can file a chargeback and automatically win (no I am not kidding). The GC chargeback system appears to be automated in this regard. GC won't even contact you beforehand, they'll just grant it and notify you you're out the money.
Last, they destroyed their only value when they moved to Paypal's graduated fee schedule (was 2% + $0.20, now it scales from 2.2% to 2.9% depending on volume). GC is still free (Paypal charges $30/mo for the same service) but for the hassle you go through it wasn't worth it to us. That, and they used to give Adwords credit once upon a time.
Paypal is no cake walk, but at least there are live humans to interact with when there's a problem. If you need a second payment system go with Paypal Express Checkout (I had at least 5x the use vs GC). I've not tried Amazon Payments yet, but they seem promising as well. I've gotten the distinct impression that GC is a forgotten project (Google has moved onto a mobile payments platform, which has caused drama because they hired Paypal devs to build it)