Status of Ubuntu for Lenovo Thinkpad Yoga
In my experience, Ubuntu boots fine, however not without issue.
Issues: (as of ubuntu 14.10)
Installation: As with all laptops with Windows 8, (pre-installed), UEFI can be a bit of a pain when installing, but this guide should get you through that with no issue.
Touch Screen: Touch screen works, but there is no multi-touch or scroll support. So for example, when you drag your finger down a website, normally the site would scroll, on Ubuntu it simply clicks the screen repeatedly. This includes the unity dash, which is odd as the interface seems quite touch optimized, but in reality is not.
Rotation: The hinge rotation causes no issues, however the trackpad does not disable itself upon rotation. The accelerometer is not supported as far as I know, so automatic screen rotation does not work either.
Function Keys: The basic function keys work, however not all of them if I remember correctly. The volume rocker and power button on the side of the laptop work, however the screen lock button does not.
NVIDIA Discrete Graphics: Doesn't work out of the box, and will not switch automatically based on the open application, but can be used. Installing nvidia-331 through the Ubuntu repositories will install the necessary drivers, as well as an Nvidia settings panel that includes the option that will allow you to switch between the low power Intel graphics and the NVIDIA graphics card. This does require you to log out and back in to restart the X server before it will take effect.
It's been a few months since I ran stock Ubuntu, so some of these things may have changed, however that was my experience.
My current setup: I'm currently running Ubuntu Gnome 14.10. Although I much prefer cinnamon or unity, I found Gnome to have by far the most support for the Yoga 14. Gnome is fully touch optimized, so things like scrolling and dragging around windows with touch work flawlessly, as well as two finger scroll and other gestures on the trackpad. All of the function keys on the keyboard work fine, including the function lock, mute key + indicator light, internal mic mute + light, and the trackpoint. It also has fantastic HDPI display support, so everything looks great on the 1080p display of the Yoga, more so than Windows 8.1, which has a huge amount of applications that are either normal size and blurry, or clear but extremely tiny. The trackpad still does not auto-disable however, and auto-rotation does not work, although I am working on finding a fix to that, as manual display rotation is available in the settings and the touch screen correctly rotates its touch points to the screen orientation. The NVIDIA driver can be installed in the same way.
I'm currently running Windows 8.1 on the internal HDD for the few left over things I still need it for, and its slightly better rotation and touch support, and I've disabled the SSD cashing and have installed Gnome on the 16GB SSD. This setup works great for me, however this may not be optimal if you plan on using linux as your daily driver. Due to this setup, I can't comment on the support for SSD cashing within Ubuntu.
Update in response to question, as of 3/26
Yes I use this configuration for regular work, and keep windows around more for entertainment purposes. 16 GB is a little small, and I store a lot of the larger data on the HDD and access it from linux, so 8GB might be a bit too small for regular work. I've been having some issues with Windows freezing at certain points like logging in, but those issues happened before my install of linux so it is probably not the cause. Other than those issues, the only slow down I've noticed vs with the cashing is slower boot time and the locational application launch taking longer than usual. Linux remains miles faster than Windows in either configuration however. My experience with Windows 8.1 has been that surprisingly, it works quite well with the yoga form factor, but the various freezes, restart requiring bugs, and general slowness make it a bit of a pain to use vs linux. If not for the half baked touch support in linux currently, I would switch full time in an instant.
Update as of 4/7/15
16 GB proved to be too small for my main OS, so I have now repartitioned my drive to contain a windows partition, shared data partition for documents, movies, and music, and a Linux partition and I have gone back to using the SSD for Windows Caching. I have created two simple scripts that disable/enable the trackpad that I use through launchers to easily toggle tablet mode. user1941046's scripts below this seem to be much more comprehensive than mine, however I have not tried them, so I can't give input on their effectiveness on Ubuntu Gnome. I have not run into any additional issues relating to the Thinkpad Yoga 14 hardware.
I have adjusted the thinkpad-yoga-script to work for the Thinkpad Yoga 14 S3: https://github.com/johanneswilm/thinkpad-yoga-14-s3-scripts . It takes care of rotation, blocking trackpad when in tablet mode and automatic brightness control (all issues that weren't taken care of hitherto).
Should we create a Wiki and update it over time on how to get the different features of the Lenovo Thinkpad Yoga 14 (2014 and 2015 editions) to work? Then we can update that over time. Either directly for Ubuntu or simply for all linux distributions.
There is some issue with the internal keyboard and newer kernel versions and the Lenovo Thinkpad Yoga S3 (spring 2015).
When going into standby, the internal keyboard stops reacting afterward some times. If one tries to reboot, the keyboard will work in the BIOS, but not at the cryptsetup login screen. After logging in to the system with a USB keyboard and booting linux entirely, the keyboard works again (most of the times). The problem is present in kernel 4.0, but only happens once every few months. On kernel 4.2.5, it happens almost every time the computer suspends.
I have not been able to find any other bug report about this. Newer kernel versions are required for some features to work, so this is a major issue.