I encounter code access security quite often in the "real world", often when I least expect it. And in a way, SilverLight would be an excellent real-world application of it, were it not that SilverLight chose not to employ CAS at all in the end.
Hosting providers
The places where you see it in action is where a secured environment is needed: ASP.NET itself of course, but ASP.NET hosting providers use a modified security model to prevent intrusion in their precious systems. I know for a fact that Webhost4Life uses this (no information on their site about it, but I've worked with them, it's there, really). Looking further, other ASP.NET hosting providers do the same, but they are not very clear about it either: thread on godaddy.com not wanting to change the CAS (and no clarity what's supported and what not) or this related discussion on 1&1. Some cloud hosting sites (rackspacecloud) took it a bit further and "worked with Microsoft for a modified full trust level" whatever that may be.
In short: if you find an ASP.NET host, most likely they've used CAS to prevent you from doing things they don't want you to do. They can even use it make difference between "basic" (many restrictions) hosting and "enterprise" (few restrictions) hosting which gives a whole other meaning to CAS.
Other applications of CAS
So much for a few real-world situations that I encountered myself. A recent project I did had something similar: allow the user to upload a library, and test it for performance ("who makes the best algorithm"). Needless to say, we needed CAS heavily there. Other examples or interesting resources:
For any situation where you are simply in full control yourself, you build your own app and code (or have it built) and are in complete control of your system, I don't think you'll need CAS too often. It's more something you'd use the minute you get to run code from lesser trusted sources (which is basically everything that's not in your full control).
CAS vs ClickOnce
Default CAS settings limit the capabilities of code run from a network share or other non-local sources. This makes sense but the stringent restrictions make it hard to have a central repository for distributed application. .NET 2.0 introduced ClickOnce, which was supposed to elevate the security (discussion here).
ClickOnce itself uses CAS, to prevent the installer from calling into system functions. As such, I believe it is arguably the best well known application that relies on CAS.
Point being: you need to understand CAS to be able to create something that can run directly from a share, or you ignore it all and use ClickOnce.
Microsoft's Survey on CAS
In 2005, Microsoft summoned a survey to find out why CAS was so unpopular, hoping to improve it to make it better applicable. Unfortunately, I couldn't find the actual survey results, other then this post somewhat detailing why CAS is underused.
CAS in another world
That post, however, does point at an intriguing niche: CAS applied to another world: Unix / Linux. They don't call it CAS, instead it's BitFrost. How's that for a real-world application: the "One Laptop Per Child" project, which relies on BitFrost as a replacement for the traditional Unix security model.
Update: section on CAS in Unix/Linux as BitFrost and section on survey.
Update: added CAS vs ClickOnce section
Update: added list of resources using CAS (and apologies for all these updates in a row!)