Why do I go through Comcast so many times before I reach a website?

This is probably a good thing.

Basically when you go to a website or other resource on the internet, you never connect point to point - you're bounced between routers. To have a connection between two systems not go between other systems, they would need to have a dedicated line directly between them. Having a dedicated line between Google and each person using it would get complex fast. Connecting point to point is not the best option except in the smallest network. Don't forget, even to connect to a system in your own LAN through a router, you need 2 hops, so 11 hops to a server that's somewhere else is pretty darned impressive

Since Comcast owns their own links for most of the way, they're using them to save on cost. In many cases Google has servers in ISP datacenters for extra speed, so this might also be a reason for using your ISPs links most of the way.

This is the internet used as designed, in a manner that ensures you have a good enough connection to your destination, at lower cost.

I am not sure Journeyman Geek's answer is what the OP's was after. I have the impression the OP knows quite well that he cannot reach any given site (for instance, Google's) directly, I think instead his question is: why are there so many hops within my ISP?

The answer to that lies in a variety of factors.

1. Sheer numbers. While all of us have at home at most a few dozens interfaces (and thus IP numbers), ISPs provide services to millions of people. To cope with these numbers, and to provide a reliable service to all, you can only expect a large degree of redundancy built into their system. Thus, you cannot expect them to have a single interface on the Internet, they probably have thousands of them; you cannot have a single way to reach the outer interface, there must a large number of independent ways to do so to obviate the evental failure of a machine along way.
2. Load balancing. The system must have a sufficient degree of redundancy to cope also with traffic congestion. Load balancing denotes the techniques used to route requests for Internet access onto different outer-lying routers, in such a way that no router is left idle nor congested.
3. Services. It is naive to assume a major ISP only provides Internet access to its customers. Nowadays, many of them offer full-fledged services designed to accommodate customers' requests concerning mail hosting, web hosting, ftp, VMs, and so on. These services must be made available to paying customers and denied to non-paying customers, just like traffic speed is provided on a per-subscription-plan basis. All of this traffic must be correctly routed.
4. Security. While some services are not security-critical, others (often those involving the largest corporate clients) are, to both the customer and the ISP. A sufficient security layer has to be put in place to prevent malicious access to well-paying customers.
5. Existence of Tier 1-2-3 retailers. As a private customer, each of us is used to deal with a single provider. However, it often happens that this provider is just the fron-man of a hyerarchy of ISPs, where the retailers (those we pay our subscription to) rent extra services from Tier2/Tier 1 wholesale ISP. These Tier 3 are often called Transit ISPs, or even Virtual ISPs when even the hardware used to provide service to retail customers is owned by the upstream ISP.
6. Peering. This is the common practice for ISPs of interconnecting at peering points or Internet exchange points, allowing routing of data between each network for free. This has the advantage of bypassing charges for the use of lines and/or equipment owned by a Tier-1 operator.
7. Accounting. Keep in mind that much, possibly all of this traffic, has to some extent be recorded (not in its entirety, of course) to determine charges each individual subscriber has incurred into. And the very same applies to Tier-1/2/3 operators charging each other for the use of their facilities.

When you factor in all of the points for a signle large operator like Comcast, you catch a glimpse of why your data packet destined to a given site may take a very roundabout route. Of these voices, the possible unavailability of a direct connection (the outcome of redundancy), load balancing, and peering (the need to take a route inside the company boundaries to avoid incurring in the charges of higher-Tier operators) figure most prominently.

As aluded to by akira, this is due to the way the Internet Protocol works. (Simplifying somewhat), every machine on the Internet is connected to the Internet through another machine. A traceroute shows the path of every machine between you and the target. In the case of Comcast, they obviously have a lot of machines working out where everything goes, and thus your traffic needs to go through a few machines. (These machines are typically known as routers).

The answer to your question is thus "because of the way Google and Comcast Interact", you need to go through a number of Comcast systems to reach Google. This would not seem hugely abnormal or problematic.

"The internet is a series of tubes." - Former United States Senator Ted Stevens (R-Alaska)

Although Ted Stevens is incorrect in his description of the Internet, its actually a good way to answer your question.

Think of plumbing in your house. The pipe that carries water to your faucet is quite small. It connects to a larger pipe in your yard, which carries more water. That pipe connects to an even larger pipe that connects your whole street. That pipe connects to a even larger pipe that connects your neighborhood to the pumping station... etc...

Each of those "servers" are routers that are like the junctions of pipes, regulating the flow of data. Each one has a certain capacity and is placed both logically and physically to connect everyone to the internet.

Now imagine if everyone your faucet had a direct connection to every water source on the planet (every website). The sheer number of pipes would be massive and impossible to maintain. Now imagine that for every house on the planet.

What if Google went down? Then all those direct connections to them would be broken. You - and everyone else in the world - would have to run new pipes to them. That would be a massive undertaking. However, in its current set up, Comcast can just reroute a few lines and everyone would be connected again.