The New York Post (of all places !) features a Star Trek "Video Quiz" on the front page of its website, interlaced with clips from the original episode. Careful, some of the questions deal with subsequent movies, and not the original series.
http://www.nypost.com/entertainment/comicsgames/popjax_game.htm?gameId=1593&campaign=NYP_PCW_20090805
And, if you want to watch some full-length episodes, including at least one in HD, go to the CBS website here. Thanks CBS !
http://www.cbs.com/classics/star_trek/