Should I upgrade Ubuntu kernel ?

Each releases ship with different kernel version

Here is the list of the Ubuntu releases and their corresponding kernels.

How to the version of the running kernel?

The official version of an Ubuntu kernel is found in the /proc/version_signature file. This file contains both the full Ubuntu version of the kernel and the mainline version on which it is based:

$ cat /proc/version_signature
Ubuntu 2.6.35-6.9-generic 2.6.35-rc3  

The first field is always Ubuntu, the second field is the Ubuntu kernel version, and the final field is the upstream version

Linux Kernel Update policy

In almost all the distros that are not rolling release based (rolling release based = Arch, Gentoo, etc) the policy is: maintain the kernel version that was released.

Ubuntu LTS have five years of support so, Canonical give us the LTS Enablement Stacks that provide newer kernel and X support for LTS releases. For example, after 14.10 release, the kernel from this release will be available to 14.04.

But since 14.10 is not a LTS release, it's kernel V3.16 will only support for 9 months. So, it's not a good idea to upgrade to this version.
Ubuntu Kernel Support diagrams

Safe Practice
  1. Stay with the default kernel.
  2. Upgrade to a higher kernel release only when you have a solid reason(e.g., fix hardware issue or performance improvement) and skillful enough.
  3. When have to upgrade, better choose next LTS release kernel(v4.4 from 16.04) when it's available.