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1.
Exaiming anothers body, especially chest, crouch and butt regions. Usually people do this to stranger but occsionly to people they know. Usually done somewhat discreetly
The guy at the park was checking out the hot girl as she walked by
de Santas Sexy Helper 28 juillet 2004
 
2.
to commit suicide; to end your own life,

stems from checking out of a hotel, checking out of your own life, choosing to leave.
i fucking gone im gone im gone, so im checking out. im checking out real soon.
de john gold 15 mars 2007
 
3.
a term used on instant messaging services. meant as "im gunna go"
urscreenamesuks: yo, im gunna check out, i'll catch ya lata
de morgan 16 avril 2005