I find myself separating this into two categories: how I look at the work of others, and how I look at my own.
For someone else's photographs, I am willing to accept a broad range of photographic techniques, from the conventional to the bizarre, if the end result is appealing to me. Many of these approaches are far beyond what I would attempt in terms of deviations from straight photography; the impact of the end result is what matters to me, regardless of how a particular photographer got there. That said, heavy-handed post-processing - a sort of modern-day pictorialism - is almost always unappealing.
In my own work, I'm pretty restrained in terms of using "effects" (not a great term, but the best I could come up with) for the most part. I like to subtly isolate subjects with depth-of-field when appropriate, occasionally shoot contre-jour for flare and low contrast, and maybe a little long exposure motion blur every now and again. Beyond that, my work is relatively straight and focused primarily on form and subject. I'm dissatisfied on a certain level if the photo suffers from technical "effects" that I did not envision and purposely invoke, even if the end result is interesting. "Happy accidents" are always somewhat frustrating to me because they are uncontrolled and thus unrepeatable.
