I do but only one character specifically right now and that's Inoue-chan from Bleach..I'm not sure why the name just caught on with me more..also Hayato-kun (Gokudera-kun) from Katekyo Hitman Reborn also I'll refer to Megure-san and Mouri (Kogoro) -san (from Meitantei Conan) by their last name rather than their first but there are others..but those are the main characters that I do it with.

When an anime is dubbed they usually change it to first name, since I'm a dub person calling by last name is just weird for me! However I watch 2 animes subbed before and lots of people are called by their last names. That's when I use their last name! In other cases it's just weird for me to call a character by their last name!

Sometimes it's just easy to remember or is just catchy than the first name x3

sometimes i refer them to their last names if i don't like his/her first name!

it depends whether i watched it on dubbed or original audio.

but i think Kuwabara from Yu Yu Hakusho doesn't count sine almost everyone calls him that.
And Kanda from D.Gray-Man since he will definitely slice me if i call him Yu.

for characters with foreign names other than Japanese usually it's the first name!

Nah, I just find that confusing. I prefer saying the character's first names only, but that's just me.

I call Takashi Natsume from Natsume Yuujinchou Natsume.