Presenting a nice assortment of lightweight yet fully functional Linux distros for all occasions. All of these are full distros that do not depend on cloud services; four for x86 and two, count 'em, two for ARM hardware. (Updated Feb 2016.)
Elementary OS is a beautiful, fast, lightweight Linux for 32- and 64-bit x86. It is built on an Ubuntu core, and Elementary's desktop environment, Pantheon, started out with some stripped-down GNOME 2 elements. But, it is more than an Ubuntu respin or GNOME fork -- a lot of custom development goes into Elementary OS, including apps and its development toolkit.
Elementary OS has a Mac-like feel with a sleek, elegant appearance, subtle highlighting cues, minimal clicks to get from one place to another, and lots of useful super key shortcuts. I expect that even inexperienced Linux users could start using Elementary OS and be productive with just a little bit of poking around. One feature that sets Elementary OS apart from other distros is the extensive documentation for contributors. It covers interface design, coding style, building apps, and everything else you need to know.
There are currently $6,055 of cash bounties available for bug-fixing some applications and base libraries. If you can't code, putting a few bucks in the bounty kitty is a great way to support Elementary OS.
LXLE takes Lubuntu LTS (long-term support), customizes the LXDE desktop, adds proprietary codecs and drivers and a thoughtful selection of default applications, and advertises it as a drop-in replacement for Windows. Me, I think anything is a good replacement for Windows, including an Etch-a-Sketch. But LXLE (Lubuntu eXtra Life Extension) really is an excellent choice for users who want to swap Linux for Windows.
LXLE is not an amazing new revolutionary technology, but rather an excellently crafted and refined enhancement of Lubuntu 12.04 and 14.04 optimized for older, less powerful PCs. (The newest release is 14.04.3.) The last 5 percent of any project is the hardest, and LXLE goes all the way and finishes that last 5 percent. Installation is fast and simple, and it boots up very quickly -- in under a minute. LXLE has five desktop looks to choose from: Unity, Windows XP, GNOME 2, Mac OS X, and Netbook. Its most fun feature for me is the 100+ included beautiful wallpapers, and the Random Wallpaper button to cycle them automatically. Windows refugees, or any casual user, will find their way around easily. It also includes the full capabilities of Linux for power users. That is why I love Linux: we can have it all. (32- and 64-bit x86)
Arch Linux ARM
Arch Linux is the choice of fine nerds everywhere who want a simple yet versatile, up-to-date, lightweight rolling distribution. It is always among the first distros to package new software releases, such as PHP 7 and KDE Plasma 5.5. Arch calls itself simple because it comes with a minimum of bells and whistles, and it is for users who want maximum control of their systems with no backtalk from "helpful" utilities.
Arch supports x86 and also has an excellent ARM port. ARM devices are everywhere thanks to single-board computers like the Raspberry Pi, BeagleBoard, and Arduino, smartphones, tablets, and netbooks like the Samsung Chromebook. Arch is extremely customizable, so you can pare it down to fit even the smallest SBC and make it into a router, a special-purpose server, or even a tiny but useful portable desktop computer. Just like x86 Arch, ARM Arch is well-documented and has active community support.
Point Linux is going on three years old and is still under active development, which is good for a newcomer. Originally, it was based on Debian 7 and the MATE desktop, which was originally forked from GNOME 2. Now, the good Point Linux people also support the Xfce desktop. It has a traditional system menu and panels -- nice and clean, and everything easy to find with no dancing icons, no hidden things that appear only when you luck out and hover your cursor over exactly the correct spot, and virtual desktops that stay put.
It runs well on old feeble hardware and now offers multiple download options: 32- or 64-bit x86, and full or minimal core versions. Point Linux is based in Russia and has good comprehensive localization. If you miss the Ubuntu of old, when it had the best GNOME 2 implementation of any distro, then you might like Point Linux.
Good-bye Porteus, Hello Android-x86
Porteus is nice Slackware remix that runs from a USB stick. However, it hasn't had an update since 2014, so I'm replacing it with Android-x86. Android-x86 ports Android to x86. It originally began as a set of patches for the Android Open Source Project and is now a complete Android operating system for x86. You can download the live ISO to either run it as a live image or install it to hard disk, or you can get the .img download to run it from a USB stick. Android-x86 is great for x86 tablets, netbooks, and ultra-portable laptops.
Android-x86 is 100 percent open source. If you're looking for an active, important project to contribute to, consider this one.
Fedora's ARM port was promoted to primary architecture status as of the Fedora 20 release, so it tracks the Fedora x86 releases. The current release is Fedora 23. In typical Fedora fashion, ARM support is broad and pushes into the bleeding edge with support for 64-bit ARM, all the popular ARM SBCs, and a nice selection of unofficial remixes for unsupported devices including the Samsung Chromebook. Which I keep mentioning because it looks like a perfect travel notebook once you clear the Google gunk off and install a good proper Linux on it. Visit the Fedora ARM wiki page to learn everything.