Yes, but not frequently. You're most likely to hear it in fantasy novels(slaying dragons), metaphorically in a sports headline (team X slays team Y), or in the passive in an headline about a murder (X slain by Y).

"Slay" sounds slightly archaic, but there are still situations in which we use it. It's connected with the word "slaughter", if you were wondering about it's relation to "kill". "Slay" can also mean "overwhelm with delight" and surprisingly this is quite an old usage of the word and closer to its original meaning, "to strike". For example, "slain by her beauty" and "slaying them in the aisles" (referring to a successful comedy act). Modern speakers would assume the "slay" is figurative.

Examples: "Not only must he fight with and slay this golden-winged, iron-scaled, long-tusked, brazen-clawed, snaky-haired monster, but he must do it with his eyes shut..."--Nathaniel Hawthorne, "A Wonder-Book for Girls and Boys" "And hast thou slain the Jabberwock?"--Lewis Carroll, "Jabberwocky." Notice that "hast," "thou," and "slain" are all archaic--he is being intentionally archaic, to give his poem an epic sound. Here's a good example. In the traditional English translation of the Bible, the "King James Version" of 1611, we read that "with the jaw of an ass have I slain a thousand men." In a popular modern translation, the New International Version, written in clear modern English, the same sentence is translated "With a donkey's jawbone I have killed a thousand men."

"Slay" and "kill" are close synonyms. "Kill" would be the normal word. "Slay" is old-fashioned. It is a word that most English speakers understand--and need to understand because they read it in books--but would not use. "Slay" might be used if you _wanted_ to sound old-fashioned; if you were writing a fantasy novel you would not say "he was a dragon-killer," you'd say "he was a dragon-slayer." The entertaining mystery writer, Dick Francis, wrote a novel called "Slay Ride," which is punning on the word "Sleigh," which is pronounced exactly the same way. A sleigh or sled is a vehicle with long steel blades instead of wheels, for traveling on ice. In the novel, the bad guy tries to kill the good guy while they are riding in a sleigh, and so... the sleigh ride is a "slay ride."

"Slay" is not a common word in English.