Distinctions need to be made. After all, there are many different types of series*:
- The stand-alones: These are series that center around a shared world that have no established, continuous plot from book to book. Terry Pratchett's Discworld series is a great example - a reader can start with just about any book in the series and not feel like they're missing much. It's a series, yes, but each book is a stand-alone. The same for Émile Zola's Rougon-Macquart books - some characters may appear here and there, some locales are familiar, but there is no need to read L'Assommoir in order to enjoy Germinal**.
- The character stand-alone: I find this for the most part with mystery books - a series will follow the happenings of a specific detective. Each book can stand on its own, but it helps to have read previous books, if only for the character development.
- The continuous epic: This would be something like A Song of Ice and Fire, which can often feel like one supremely long book cut up into little (or, uh, huge) pieces. It's hard to distinguish one book from the next, and absolutely impossible to miss a book in the series. There is no single, contained plot within each volume - at times it seems like there's absolutely no justification for it to be a separate book other than length (A Feast for Crows/A Dance with Dragons, anyone?).
- The planned series: A planned series is exactly what it sounds like - the writer goes into the story knowing exactly when and how the story will end. It's defined ahead of time as a trilogy (or a quartet, etc.) and sticks to it. Each book may blend into the next with cliffhangers, but there are still clear-cut boundaries between each volume. This is something like His Dark Materials - the books are individual and contained but are part of an undeniable whole. You can't read the second book without having read the first.
- The contained epic: A contained epic would be something along the lines of Harry Potter. There's an overarching story and you can't read one book without having read the previous, but each book still contains its own, individual story that doesn't really drag onto the next book (though the lines blur a bit with Half-Blood Prince and Deathly Hallows). This is the the planned series taken to the extreme - a long, sometimes meandering and less defined series but contained nonetheless.
- The popularity mess: Books that should be stand-alones or part of planned series and eventually degenerate into a continuous series because of poor planning. These go on until they fizzle and are an embarrassment to themselves. Please let's not raise examples. It's too depressing.
But beyond the simple breakdown of series type, you have to look at intent. Is this a series simply because of length (a story on such an epic scale that it demands multiple volumes)? Or is it something inherently episodic? If you're the type of reader who decides whether or not to get involved in a series, it's important to pay attention to these qualities.
Personally, I don't really care if a book is part of a series or not. It's never been a factor for me. While I don't like ditching series halfway through, I'm not entirely averse to it. There are a few series I've given up on after realizing that the books I'd already read within them stood alone fairly well and didn't entice me enough to keep reading. If the first book was bad and I don't have to read the sequels, I'm not going to go on. As I learn to abandon books, it becomes easier to stop midway through a series. And really, it doesn't matter if it's part of a whole or not... it just matters if it's good enough to make me want to finish the series.
* And yes, I did notice that almost all of my examples are from fantasy series. What can I say, that's what came to mind...
** But you should. Read both books that is, because they're excellent.
** But you should. Read both books that is, because they're excellent.