You can safely install the Kernel 3.15 or 3.16 in Ubuntu 14.04 which offers you some benefits.

The biggest benefit is that from Kernel 3.15 the 3th Generation Haswell Intel i5 and i7 processors are better supported, which include the graphics and some of the additional processor instruction sets.

The safest option is to install Kernel 3.15.10 especially if you have some Vmware and a add-on graphic card that need Kernel specific modules to work correct.

As running the 3.15 or 3.16 Kernel is only useful for users who have a Intel 3th Gen. Haswell i5 or i7 I will only give the how to for 64 bits Kernel.

Open terminal and create a folder TMP ($mkdir TMP), after that goto the TMP folder (cd TMP) and download the files needed to install the 3.15.10 Kernel for Ubuntu 14.04 by entering line for line....

wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.15.10-utopic/linux-headers-3.15.10-031510-generic_3.15.10-031510.201408132333_amd64.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.15.10-utopic/linux-headers-3.15.10-031510_3.15.10-031510.201408132333_all.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.15.10-utopic/linux-image-3.15.10-031510-generic_3.15.10-031510.201408132333_amd64.deb

After that run

sudo dpkg -i linux-headers-3.15.10-*.deb linux-image-3.15.10-*.deb

When this is finished just restart your computer (sudo reboot)...

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For the more adventurous people you can also install Kernel 3.16.2

Open terminal and create a folder TMP ($mkdir TMP), after that goto the TMP folder (cd TMP) and download the files needed to install the 3.16.2 Kernel for Ubuntu 14.04 by entering line for line....

wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.16.2-utopic/linux-headers-3.16.2-031602-generic_3.16.2-031602.201409052035_amd64.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.16.2-utopic/linux-headers-3.16.2-031602_3.16.2-031602.201409052035_all.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.16.2-utopic/linux-image-3.16.2-031602-generic_3.16.2-031602.201409052035_amd64.deb

To install run:

sudo dpkg -i linux-headers-3.16.2-*.deb linux-image-3.16.2-*.deb

I have Kernel 3.16.2 installed on my Asus Z87M-Plus with Intel i5-4670K and it works perfect...

I installed the latest kernel on my i5-460M machine a few weeks ago, then overwrote the installed Virtualbox with the latest version... sudden death!

Only circumstantial/by-association evidence, but good for young players to not wipe your older kernels for a while... AA

The instructions do not overwrite or remove the previous kernel so anybody would be able to start with the previous kernel without any problem.

I use Oracle VirtualBox 4.3.14 with Kernel 3.16.2 and have no problems at all. Also I cannot understand how generating new kernel modules will result into a sudden death