The phenomenon that is "Star Trek" is rather difficult to encapsulate in one short article. There have been television shows, movies, novels, reboots, merchandise, cosplay and more, dating from the debut of the original series (ST:TOS) in 1966. The cultural impact of the series is impossible to estimate. But, we're going to give it a shot, and we're starting with the basics.
"Star Trek," now known as "Star Trek: The Original Series," aired from 1966-1969. It was soon followed by "Star Trek: The Animated Series," which ran from 1973-1974. The show then returned in "Star Trek: The Next Generation," in what might be considered one of the first reboots in 1987. It ran till 1994 as a syndicated series.
Then came the spinoffs, which some argue killed the series simply because of the ubiquity of "Star Trek." "Star Trek: Deep Space Nine" (1993-1999) was the first series set in a stationary location, and the first with a black captain. "Star Trek: Voyager" (1995-2001) featured a spaceship that was forced into another sector of space, thus giving its crew a new area to explore. It featured the first female captain. And "Enterprise" (2001-2005) went back to the earlier days of the Federation. These last two series aired on the fledgling network known as UPN, which was shut down in 2006 (some of its programs then moved to The CW Network, which rose from the ashes of another fledgling network, The WB).
To date, there have been a total of 12 feature films, if you count the last two directed by J.J. Abrams. The first, "Star Trek: The Motion Picture," was released in 1979 due to the efforts of creator Gene Roddenberry and the success of TOS in syndication. "Star Trek II: The Wrath of Khan" followed in 1982. "Star Trek III: The Search for Spock" came out in 1984, and "Star Trek IV: The Voyage Home," was released in 1986. "Star Trek V: The Final Frontier" from 1989 is often considered to be the worst of the TOS films, and "Star Trek VI: The Undiscovered Country" spouted a bit of Shakespeare in 1991. Of these movies, the best are considered to be the even-numbered films. Fans who saw these films in the theaters (like me) certainly remember the despair of Spock’s death and the cheers when he returned.
The next four films feature the cast of “The Next Generation,” with the first, 1993’s "Star Trek Generations," bridging the gap between the original cast and the TNG cast. "Star Trek: First Contact" was a 1996 effort, and "Star Trek: Insurrection" came out in 1998. "Star Trek: Nemesis" from 2002 was the last of this era of movies. Most of these were considered solid efforts, but nothing culture-shattering.
After all the "Star Trek" TV series left the air in 2005, there was a gap of about four years without a single official "Star Trek" property appearing onscreen before J.J. Abrams helmed the reboot, based on the characters of TOS. Spock, Kirk, McCoy and others were portrayed by younger actors in the movies "Star Trek" from 2009 and "Star Trek Into Darkness" from 2013. These movies have been considered very successful, compared to the hit-or-miss results of the earlier films - but also have been criticized as turning away from the franchise’s philosophy, sophistication, and optimism.
Recommended Order of Viewing
Please note that if you are watching "Star Trek" for the first time, it isn't actually vital to watch everything in its exact order. However, the time frame does overlap when you get into the late '80s and early '90s series, at the point where two TV shows, "ST:TNG" and "ST:DS9," and the films were running basically concurrently. There is at least one later "ST:DS9" episode in which the plot depends upon a visual clue introduced in "First Contact." So, it is at least recommended that "First Contact" is watched between the fourth and fifth seasons of "DS9," and that you've seen most or all of "ST:TNG" before watching "First Contact" since it continues the lives of the "ST:TNG" characters.
In general, the original series and "Enterprise" have no such conflicts. "Voyager," because it takes place in the Alpha Quadrant far from Starfleet territory, also doesn't contain as much overlap, although it does use the universe as developed in "ST:TNG" and "ST:DS9." Many consider "ST:NG" the easiest to get into if you're new to the "Star Trek" franchise.