I never really thought about why I love Startrek and as a matter of fact I am one of the rare species that loves them all, ToS, TNG, DS9, Enterprise.
They all got their charme and moments and also got their downsides and boring episodes.
I think the beauty lies within the creation as whole. It is on one hand fascinating because its a working world, like Tolkien created and on the other hand it is mankinds dream.
Seriously, everone sane in some way desires the world StarTrek takes place in.
World Peace, no poverty, one unified goverment, no hunger, no desease and a society based on sanity and commonwealth, in an non aggressive alliance to hold those values dear and spread it in the galaxy, driven further by the hunger for knowledge to find the final answers…
Who hasn´t hated Picard once for doing the right thing thinking he´s a selfrighteous brick but in the same instant admireing him for doing so? 
Who doesn´t love Kirk for using his fists over his mind but doing the right thing in the end anyways?
And the fictional but conclusive science makes the concept feel so graspable. If we only had a Dilicium chamber, can it be so hard to create a warp bubble… transporter beam, sounds so easy, food synthesizer seems just a matter of energy production and computational power.
And without any doubt, StarTrek inspires many scientists for decades, I tend to say it made many people decide to choose the path of science.
I for one salute to Roddenberry for his visions and got to thank him for years of entertainment and inspiration.
That said, I am no trekkie. I have no fake tricorder, never was on any convention, nor have any fanarticles other than the DVDs or can talk about maps fans made of the alpha quadrant or stuff like that. I just find it a very inspiring universe he created, a hope for mankind…
And one thing’s for sure, if the Vulcans are out there, at the moment they would laugh at us, if it was in their nature, rather than landing and extending their hand because with the current path our dustball´s on we´ll do anything but to live long and prosper 