Jisho

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Stroke order doesn't truly matter unless you're being tested on stroke order. Sometimes there are small details in stroke order that even Japanese people forget, but following general guidelines (like going from top to bottom, left to right, closing strokes last, piercing strokes last) will get you basically all of the beneficial aspects of stroke order without worrying about the specific quirks for individual kanji.

In my personal opinion stroke order is actually very important.

Especially for handwriting. Even if the writing looks like chicken scratch you can usuallly rather easily figure out what something is supposed to look like. That is, if they follow the stroke order.

As I said, general stroke order concepts will get you the benefits you're referring to, but I don't recommend obsessive memorization of every kanji's individual stroke order quirks, unless you are planning to take the Kanji Kentei, or your teacher cares about it, or if you're doing calligraphy or something.

Yeah, stroke order is not very important in everyday life. Sometimes, the radical 口, such as in 言う, can often be written with ○ if you are handwriting it. It just seems much simpler to use one continuous stroke versus 3 separate ones. However, there are cases when stroke order can be useful. One such case is 右 vs 左. The first stroke for both of the characters is different, and that's done specifically to help you write without putting you in an awkward position as you write. But like stated, it's not necessary (unless being tested), so just write the way you feel.

Stroke order is important in certain situations. It's true that if you're studying Japanese and you write a kanji slowly and carefully in the test with incorrect stroke order, the teacher may not be able to tell. But if you want to be able to have good handwriting in Japanese and you want to be able to write quickly, correct stroke order is important, because when you write quickly or messily the strokes will blur together in into one (such as the example given by Jonathaneng93). Many Japanese will write it so it looks like a circle. I write it so it looks like a circle. But my circle (and those of the Japanese) will always start on the left and go clockwise. Stroke order creates consistency when your handwriting is fast or messy, and it will allow Japanese to still be able to read your handwriting when it's fast or messy.

What does everyone else think?

My personal observation over time has been that handwriting that follows stroke order tends to be more legible than handwriting that does not.