The other day, I was watching Star Trek (the original series, naturally) and I thought of two interesting questions. The first was “what would Star Trek be like if it got commissioned now as a new television series?” The second was “what would be different about today’s culture if Trek had never existed?”
The effects of the new series would be much better for one thing. Gone are the days where you can redress your regular set and put up some curtains to depict an alien ship ("The Corbomite Manevuer") and the truly bad effects (and bad episodes such as "Spock’s Brain") would be mocked within minutes of the airing on the internet forums. 
The seasons would work on a more arc-based layout, with ongoing narratives driving the plot, much like 24 and Heroes did and several other shows still do. There would be more than one two-parter throughout the entire series and the show would most likely be unnecessarily dark and gritty (following the trend of films since 9/11).
And I would hope that blatantly sexist lines such as "Believe me, it's better to be dead than to live alone in the body of a woman," as well as acting like a Nazi to a German officer because of his name (one of the plot holes of “The Squire Of Gothos”) are just some of the things that would never get past the censors today, but with the existence of Quagmire from Family Guy and Barney from How I Met Your Mother it's hard to say whether they would or not.
If the look of the reboot movie is anything to go by, the ship would look a lot more hi-tech than it does and the look of a tricorder would owe a whole lot to the iPad. The uniforms would be a lot different, as the original costume designer died a while back (this means velour would no longer be the order of the day). While the amount you can show on television has changed since then, the women wearing those costumes still manage to look appealing today, which is quite an achievement. In the episode "Requiem For Methuselah", the character of Flint would not have worn some kind of laughable cape and tights combination.
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Article comments
1 - Dr Dreadful
Small point of order: Mae Jemison was the first African-American woman in space.
The honor of being the first African-American in space arguably goes to Guion Bluford, Jr, who was a member of the crew of STS-8 and three other Shuttle missions.
Arguably, because the first black man in space was actually one Arnaldo Tamayo Mendez, a Cuban who took part in a Soviet Salyut 6 mission in 1980.
2 - Scotty2
Ah, interesting. You learn new stuff every day.
3 - myOSH
bear in mind the series is developed from 60's. And there is a lot of technology nowday where it is impossible back then. However there is a lot of effort I see in the remastered series of Star Trek where they try to make it more life like in this century.