Not to me, if there is a sequel I don't like then I don't bother buying just so I have a whole trilogy on dvd seperately. I do have all three Terminators though because I got the third as a present for Christmas when it came out and I missed it at the cinema.
It depends on the series really. I recently bought the Star Wars Prequel Trilogy just to complete my collection. But I never got the last two Halloween movies or the first two Scary Movies because they're crap.
I have the first Texas Chainsaw Massacre, the third, and the remake. I've been considering getting the 2 and 4 to complete the collection. I can get 4 for real cheap. Then I'd get 2 just to complete it. I wouldn't get the remake prequel though.
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I may never buy a dvd ever again. I just don't watch the ones I own anymore, except a few like The Big Lebowski and The Star Wars Tril. A while ago I realized that video stores are basically my movie collection. I can go and rent any movie I want at just about any time, and I don't need to spend more that two dollars. It's rare I watch a movie over and over, and that is what I figure; if you know you will watch the same movie more than ten times, then you may as well buy it, which is never the case for me anymore.
While your logic is sound, as I have well over 1200 DVDs (about 125 purchased, rest burned copies), I rarely dig into my binders to watch something I have archived anymore. The Big Lebowski (all cool people watch this film over and over) and Conan being movies I pull to watch at least once a year; maybe a couple others.
I do keep burning what I rent through Netflix, it's just a habit I guess.
I like owning all the films I like, I tend to watch a lot of single scenes in a film over and over, and knowing that I have that film in my collection and I can watch my favourite scenes whenever I want without waiting makes me happy
To answer the original question, no you don't need to own all the films in a particular series. But it's up to you. For example, I own Terminator 3 to "complete the collection," even though I hardly watch it. Same with some other movies. It doesn't make any logical sense.
As far as renting vs. buying, there is something to be said for owning the actual dvd's and having a collection that represents your tastes. I take pride in my dvd collection. I pretty much agree with Wolfie on the renting, I usually do it if I've never seen a film before/don't plan on seeing it again. I do own movies that I watch pretty regularly though, which is a benefit of owning them.
Extinction was better than the second Resident Evil movie. I bought the second one because it was out on dvd before it reached cinemas here if I remember, crap movie but keeping it because I like the opening of the film, and the DVD packaging. Not buying the third one though to complete.
What I can't stand, is the same goddamn movie being re-re-re-released in order to make more money. I.E. the damn Star Wars Trilogy. I like the SW films, they're pretty cool, but how many times have they been relased in special editions, combined editions and older editions in counting. I won't buy into all that.