Well... It depends...

I would argue that yes, you should include your business name within your home page's <title> tag (if your brand is relatively unknown) but not on internal pages.

No...
Home Page <title>Business Name | Keyword Optimized Title</title>
Internal Pages <title>Unique Keyword Optimized Title | Business Name</title>
Yes...
Home Page <title> Keyword Optimized Title | Business Name</title>
Internal Pages <title>Unique Keyword Optimized Title</title>

I would remove my business/website name from internal page's <title> tags because I don't want useless keywords in every page title on my site.

Each page of your site should be optimized for a unique set of words. If you always include your business name in your page titles you are diluting what your web page is about (at least in most search engine's eyes.) (Search engines display the page titles on the search results page, page titles are what searches see first)

If you are the recognized authority in your field, including your business name in your page titles can increase your search traffic.

For example, which search result would YOU click on?
1) When To Service Your Motorcycle
2) When To Service Your Motorcycle | Harley-Davidson

It really depends on your company, website, popularity, size and several other factors.

Become the recognized authority and the rest will fall into place.
Don't miss: Guerrilla Marketing - Jay Levinson and Guerrilla Marketing Part 2 - Jay Levinson
Who want's to be "the small guy" anyway?