I do not read in order, but I have a system for how I read. And that system is based on my intent for reading the material.
a) NO INTRODUCTIONS OR OTHER CRAP NO MATTER WHAT: I skip the introduction, prologue, whatever. I don't want other fools telling me what to think. If it's for fun, for a project, for a paper, or whatever, it doesn't matter. Intros and the like are taboo for me.
b) READ INTERESTING THINGS FIRST: If I think a particular chapter is useful to my research/paper/general knowledge, I will read that first to satiate my curiosity; otherwise, I will not be able to focus on the rest, having ants in my pants to get to that part anyway.
c) READING THE BODY OF THE TEXT: I will read the rest either very intently if I find the material interesting, or in a skimming/speed-reading fashion if I have a ton of material to get through.
d) NOVELS: If I am interested in a novel, sometimes I cannot wait, and read the end when I'm in the middle. Or I will skip over a boring section. Or I will browse for a more interesting section. When I was a teenager and full of hormones, that meant the 'love scenes' (yes, I admit!); now it usually means skipping a bunch of mumbo-jumbo shit about the scenery because I really want to imagine it myself.
However, this typically works against me in mysteries because I will miss some 'crucial detail,' and then be pissed that I could not work out the end. I used to think, "FUCK, do some people actually figure these things out??? Shit. I miss all the 'important' stuff, which seems like trivial bullshit to me." As a result, I suck at figuring out mysteries.
e) UNIVERSITY PREP: If I have 200 pages of reading due by Monday, and I have been procrastinating (or if my prof is evil and gives 200 pages due in two days), I will definitely read the first and last sentence of every paragraph, as the main idea is ALWAYS in either the first or last sentence. Then I scan the rest like the scanner on a printer.
I CAN RECOMMEND ONLY THIS METHOD FOR PEOPLE DROWNING IN READING. IT REALLY WORKS!!!!!! NO PROF WANTS THE DETAILS ANYWAY: HE WANTS YOU TO UNDERSTAND THE GIST.
f) SOURCES FOR PAPERS: If I have a book that I need as a source for a paper, I will inevitably scan the index for keywords that could help me, and go directly to those pages, scan the pages for interesting info, and read more intensively if I find keywords popping up that could be interesting. Or I use the first/last sentence method.