The Star Trek franchise has come a long way since it was created by Gene Roddenberry. It has had many science fiction spin-off TV shows like DS9, Enterprise etc. Each spin-off has its own fan communities. Star Trek fans are generally called trekkers (Trekkie). It’s the fans that keep the franchise going.
Star Trek the original series came out when NASA was attempting to put a man on the moon asap. It was generally thought at that time that after the moon, NASA would attempt to go even further. May be that statement still holds true because now a days every one is talking about mission to planet Mars.
People like myself love the idea of space travel. Star Trek shows exactly that. It shows new planets, aliens, black holes, Vulcans, spaceships, Borgs, Klingons, etc. It generally shows a bright future for all of us. May be that Star Trek optimism is what inspires me. It gives a feeling of abundance.
One of the best things about Star Trek is that all of humanity is united against enemies like Klingons. This combination of optimism and unity has been handed down to The Next Generation and other Spin offs as well. It is this feeling of hope for the future that keeps me loving Star Trek. The two movies by J.J Abrams have the same character in addition to humor. All nerds and geeks love this franchise.