Android has come a long way over the years, and there's less incentive to install a custom ROM than there used to be. Nevertheless, the desire is still there. CyanogenMod remains the most established and well-known option around, so it's no small thing when a new device gets supported. Two devices that have recently made the list include the Verizon Galaxy S5 (kltevzw) and the GSM version of the HTC One Mini 2 (memul).
These are nightly releases, so there's no promise of stability. Anything could go wrong, and there are any number of ways you could screw up your device. At the same time, there's a decent chance things will work just fine, or at least well enough to suit your needs. If you're going to dive in, be sure to grab the Gapps ZIP so that you have access to Google apps and services once everything is up and running.