For what it's worth, I recently used a loner MacBook Pro for a week while mine was in the shop. Because I mostly use my mac to develop software for unix servers (typically using case-sensitive ext4 file systems) I decided to give HFS+ case-sensitive another try.
For me, all core OS X applications worked perfectly and I didn't notice any stability issues with the system at all. Also, most of my third-party software worked without a hiccup.
But there were exceptions. When I decide to give this a go, I already had in mind a number of programs I expected to break, and a few of them did. Most notably, ALL Adobe software refused to run. Because Creative Cloud requires that it is installed on your boot volume, a case-sensitive boot disk is a show stopper.
Generally, though, there are better-built alternatives to these brittle codebases. For example, I began using Affinity's Designer and Photo instead of Illustrator and Photoshop, which almost perfectly fit my use cases.
There were a few pleasant surprises: Backblaze continued to work and Microsoft's Remote Desktop was still able to be used.
I don't have any other Microsoft programs so I can't comment about Office apps, etc, which might be a bit iffy.
Once every few years, I totally rebuild my system from scratch instead of upgrading. I'm planning to do this when El Capitan is officially released, and I will be using a case-sensitive file system. As I see it: any software that is unable to run with case sensitivity is probably not something I want to be running at all. If there is something that I absolutely need, I can always run it inside a case-insensitive VirtualBox VM.
[[ Update 2015-10-15 ]]
I've now been on HFS+ Case Sensitive for over 2 weeks on El Capitan, and I haven't had a single issue. Of course I haven't even bothered to install the software I knew wouldn't work (Adobe), but I haven't run into an issue with any Apple software, App Store apps, or open source code. If you spend a good amount of time developing for unix systems, I'd highly recommend making the leap.
[[ Update 2016-09-23 ]]
Well, it's been about a year now, and I'm never going back. I'd encourage all developers to always use a case sensitive filesystem. Also, it should be noted that the successor to HFS+, APFS, will become the default filesystem for macOS, iOS, and watchOS next Spring, and as of now it's only available as case sensitive.