kliznuti

1. to slip; to skid
   Kliznuo je na ledu ispred zgrade i pao. — He slipped on the ice in front of the building and fell.
   Auto je kliznuo s puta zbog kiše. — The car skidded off the road because of the rain.
2. to glide; to slide
   Suza joj je kliznula niz obraz. — A tear slid down her cheek.
   Čamac je tiho kliznuo niz reku. — The boat glided silently down the river.

For a person slipping and falling, okliznuti se is more common.