You could try it with a stopwatch and get back to us. :)
Anyway, the 726 episodes are each around 48 minutes I think(assuming movie-length episodes are split up) so it would take around 573.5 hours (multiplying 726 by .79) to watch them. Each of the movies is either side of 110 minutes, so assuming they are all 110 minutes it would take a little over 20 hours to watch them all.
I decided to do some number crunching. Based on the Star Trek Encyclopedia, there are 79 Star Trek episodes, 178 Star Trek The Next Generation episodes, 176 Star Trek Deep Space Nine episodes, 172 Star Trek Voyager episodes, and 98 Enterprise episodes for a total of 703 episodes.
Based on the DVD sets for each series, each Star Trek episode is 50 minutes, 30 seconds long, TNG episodes are 45 minutes, 30 seconds long, DS9 and Voyager episodes are 45 minutes, 15 seconds long, and Enterprise episodes are 42 minutes, 45 seconds long for a total of 533 hours, 45 minutes.
For the movies, I used the DVD Director's Edition and Special Edition for all 10 Star Trek movies which comes to 19 hours, 3 seconds. Add that to the episodes and you have 552 hours and 48 minutes of quality entertainment which would take you approximately 23 days to watch, depending on how fast you can change the DVD! Admiral William Thomas Riker (talk) 23:30, September 24, 2012 (UTC)
Your forgetting the Animated Series. Two seasons.
I watch all the episodes from TNG, DS9, Voyager, Enterprise continously. It takes me roughly a year to go through them.