I am running Ubuntu server 12.04 and my fresh installation is using the 3.2.0-60-generic kernel, however when I go to https://www.kernel.org/ it says the latest stable kernel is only 3.14
I don't want to run into problems down the line.
The kernel released with 12.04 server at its outset was v3.2.
Canonical have committed to supporting v3.2 of the kernel:
The original 12.04 stack in Precise will remain supported for the
usual 5yr life cycle of the LTS release.
What this means is that the kernel v3.2 will receive security and other stability fixes throughout the 5 years of the support period.
Newer kernels are available for each point release - these are called enablement stacks and are primarily for newer hardware. You dont need to install these if kernel 3.2 is just running fine on your hardware.
Obviously, if you need to add newer hardware cards to your server you should first check that the cards work with the kernel 3.2 series. Likewise, if you image the server to install on newer hardware, then you should similarly check 3.2 compatibility.
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