Most interesting for general purposes are the number row and the bottom alphanumeric row, as these contain additional symbols and punctuation that you might want to use for an improved text appearance. For this post, I checked out several common keyboard layouts (German, US international, UK, Canadian, Spanish and French) and tried to find commonalities.
With the exception of US and Canadian, you get native typographic quotation marks with V and B (hold Shift too for single marks). German and Spanish give you French quotation marks on Y/X respectively Z/X. German has long dash and ellipses on the bottom row. C yields the copyright symbol on all keymaps. On the number row you can access proper fractions (at least if you are not Canadian) and some more with Shift. On 8, shifted, you have the trademark sign (with the exception of US and Canada). The bottom row, shifted, also provides multiplication and division signs on most keymaps.
So, the next time you need mathematical symbols or advanced punctuation, you don't always have to copy and paste from a character set viewer, possibly it's already right there on your keyboard.