How do I upgrade my Ubuntu server from one LTS version to another? Is this safe?

I like to keep all my servers running only the most stable versions of any operating system, so obviously I only run the LTS versions of Ubuntu.

I currently have a few servers running Ubuntu server 12.04 LTS. I'd like to upgrade them to 14.04. Is it safe to jump versions like that, and how can this be done?

It is generally recommended (read safer) that users of Ubuntu LTS wait until the first point release, due in July, before upgrading.

To upgrade from Ubuntu LTS on a server system (and Desktop too) before then, follow the steps listed below:

Ensure you're up to date with latest updates for Ubuntu.

Backup! Don't skip this step. Unexpected things can happen during an upgrade and you'll want to be prepared in case they do!

sudo apt-get update
sudo apt-get upgrade

Install update-manager-core if it is not already installed:

sudo apt-get install update-manager-core

Edit /etc/update-manager/release-upgrades and if necessary set Prompt=lts. Note: The minimum contents of /etc/update-manager/release-upgrades should be:

[DEFAULT]

Prompt=lts

Launch the upgrade tool:

sudo do-release-upgrade

Follow the on-screen instructions.

Slightly modified from Source: https://wiki.ubuntu.com/PrecisePangolin/ReleaseNotes/UbuntuServer#From_10.04_to_12.04

For more on do-release-upgrade and some handy options, see the man page.