Depending on where you live, Feliciano, Felicio, Felike, Feliks or Felizio may be more familiar variants.
You know I had to add a picture of Felix the Cat
Potential nicknames: Fee, Flick, Lixy, Lixer, Felly/Fellie
Origin: Latin, meaning "happy, fortunate."
Popularity: In 2010 Felix ranked #331 for boys, and the ranking has stayed in the 300s for the past decade. There were a total of 940 baby boys born in 2010 named Felix, 7 spelled Feliks, and 20 named Feliciano. Felix ranked #8 in Quebec and Germany, #11 in Austria, #36 in Sweden, #81 in Norway, and #221 in Scotland, all in 2010. In 2011 it moved up to #311 with 1,023 births. For girls, Felixa and Felixia are too have to rank or statistically summarize.
Fun fact: (1) You may recognize this name from the animated "Felix the Cat," one of the first cartoons of the silent film era, and by far the most popular. Although you can still find Felix around today, his heyday was the 1920s, and connections between Felix the Cat and Felix the baby name are dying down. (2) Less instantly recognizable is Felix Unger from "The Odd Couple." (3) This is the name of more than one saint (67, I believe), and also the name of four different popes. There was also a Felix in the Bible. (4) You can find many more famous Felix namesakes, but most are not instantly recognizable.
Alternate feminine form: Felicity & Felicia