Over the past fifteen years, I have needed to upgrade my computers less and less. In the late '90s through early 2000's, every couple years my motherboard/CPU/memory were so horribly out of date that the latest software updates almost begged me to upgrade. However, I built my last PC over five years ago (ASUS board, quad-core AMD processor @ 2.4GHz, 4GB memory), and it continues to steam along through every OS I have installed. In fact, even single or dual core PC's that date back to 2006 still have plenty of life in them. The reason is simple: computers have steadily become fast enough for the basic applications we use daily -- email, web browsing, and office applications.
Of course, back in the mid-2000's, there was no such prevalence of the cloud, much less any type of browser-based applications that lived within it. Applications and their data were stored on the PC, and thus required sufficient local horsepower and storage. Jump ahead to 2014 -- it's a very different story. Dropbox or Google Drive synchronize your data into the cloud, and Google's suite of office applications are good enough for most day to day activities. With the web browser becoming the most-used application, the requirements on a PC that is already fast enough are minimal: you can conceivably get by in life with only a web browser. In fact, the bulkiest "application" that slows down the machine could be considered the operating system itself! (Looking at you, Microsoft.)
This is the premise of Chromebooks or more recent Chromeboxes: design hardware and the OS to support a web browser in which the user does everything, and replace the standard desktop or laptop for a fraction of the cost. Companies like Google, Samsung, and ASUS are starting to sell these systems based on Chrome OS, a Linux-based variant. However, if you already have an older PC laying around, why shell out more money when you can repurpose it as a veritable Chromebox.
Peppermint is a Linux distribution that was developed under the same premise as Chrome OS, and is freely available. I discovered Peppermint a year ago when switching to Linux Mint as my distribution of choice. Mint is based on Ubuntu (itself stemming from Debian Linux), and in my opinion creates a more familiar and user-friendly desktop look and feel than Ubuntu. Peppermint, like Mint, produces a similar, familiar user experience, but aims at minimizing its own footprint so it run speedily on low-memory, lower-performance (older) systems. While Peppermint bundles some basic applications (including Dropbox), you could argue its primary app is Chromium, the open-source web browser project behind Google Chrome. More applications can be installed, but the baseline configuration is perfect for targeting a system that uses the cloud for productivity (e.g. Google's office applications). In short, Peppermint has become my favorite go-to operating system, especially when breathing new life back into 6-8 year old hardware.