Should I include a "|" for better page title SEO results?
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I am not sure the is any technical benefit however more used as Alan and EGOL suggest to separate keywords / phrases and increase CTR
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I use the pipe because SEOmoz uses it. Visually it indicates something different is following. I think it more professional looking than the mere dash.
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I think people prefer pipe symbol over hyphen..as it takes relatively less space...that's the only benefit I have seen..
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Sounds like it is just an issue of conserving valuable character real estate while being aesthetically pleasing to the reader.
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The pipe and hyphen as already suggested are the way to go for pure usability and space saving for your title tag. In my opinion neither has a direct SEO advantage over the other however they both have a distinct advantage over other techniques. For me keeping the keywords used in the page title to the point help without any extra "by, or, and" breaks the keyword blocks both visually and semantically for the search engines. Now don't get me wrong I don't think this makes or breaks a good SEO effort on a page but for me it's certainly a preference.
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| has my vote! More for readability than anything.
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| has my vote! More for readability than anything.
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When it comes to a web page Title Tag Google's Supper Smart Spiders pay no attention to the markup or punctuation used. So it truly comes down to the personal preference of the site owner. As for me and my OCD I prefer the Pipes cause they just look cooler!

To prove this point query the following:
allintitle:"-"
allintitle:"|"
allintitle:"/"
allintitle:""
allintitle:","
All come back with BUPKIS
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SEO advantage I would suggest is negligible, if any in this case - more a case of aesthetics as has been suggested, as well as character count saving.
Section pages I would go with "Section | Company Name"
Product pages I would go with "Product - Section | Company Name"
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I always prefer the pipe for the following reasons, though I don't think it has any specific SEO value.
a) its reader friendly
b) its a natural separator
c) as Seth says below, it looks cool!
d) Whats good for SEOmoz is good for me!