Is it possible to obtain a complete collection of Star Trek products? Not just every episode and movie, but every novel, every reference book, every comic book, every action figure and every newspaper comic strip?
Is there even a market for old newspaper strips or do they all get thrown away?
More likely they get reprinted in book form. There's at least one on Amazon right now.
As to the question, sure I imagine it's possible, but for me, the real question is how practical is it? For one thing, there's the cost of actually buying everything, then there's the matter of storage, which, depending on how you go about it, is more cost.
Then, there's individual interest. I'll use myself as an example. I own all the DVD's of every episode and movie ever made, except Into Darkness, but that will change come November. As well as all the soundtracks currently available on CD. I also have every novel ever published because I like to read. I have the companion books for the episode guides and behind the scenes info, but other reference books such as the Star Charts and similar books don't hold my interest.
It's the same with collectable glasses and other knick knacks of that nature. Zero interest. Same with the toys. if they had had those things out when I was eight years old (when I was collecting the Star Wars toys and the old plastic bridge TOS set with the figures), then I'd be interested. Now, no. I do have the 1993 gold ENTERPRISE-D sitting on my entertainment center next to my TV, but I keep that mainly because it was a gift from my mom (the person who introduced me to Star Trek when I was a baby), who has since died. I also have several of the Christmas ornaments from 1992-2003, which were also gifts from mom, but after she died, I stopped collecting those. My friends tried to keep up that tradition for a couple years afterward, but it just wasn't the same.
So, I guess what I'm saying here is that it really depends on what you're really interested in.