What is sans serif?

In recent years the previously obscure field of typefaces has become increasingly fashionable. Seth Stevenson at Salon suggests that 'font fanatic' Steve Jobs was a crucial influence in the rise of the 'amateur typography expert'. 

To join this groovy world of graphic design you first need to identify the difference between serifs (those with 'little feet') and sans serif (those without).
sans-serif typefaces (with no little feet at the tops and bottoms of their letters) first appeared in the mid-1800s, they were labeled "grotesque" because they looked quite bizarre to unaccustomed eyes.

Serif V Sans Serif

Traditionally, sans serifs are used for headline rather than body text in print. The rationale is that the serifs help the eye to distinguish words. But increasingly this approach is challenged by some typographers - with the rules being deliberately subverted by the 'grunge typography' of David Carson, for example.
'The End of Print' by David Carson

Many feel, however, that the radical approach of Carson fails in the first objective of typography: legibility. It should be noted that a serif typeface,Times New Roman is still the default font for the world-conquering Microsoft Word. Standard sans serifs (generally seen as more informal and modern) like Arial and  Helvetica are ever-present in the commercial world, particularly in signage, logos etc. 

Another sans serif, Verdana, is very popular for online text - you are reading it now. It was designed for Microsoft in the 1990s for this purpose

Best typefaces? Worst?

Typographers will haughtily telly you that the better question is 'best for what?'. Interestingly Times New Roman still has high status and Helvetica also retains its prestige. Universal loathing, however, is reserved for that staple of a million school handouts, Comic Sans. Hence this joke: 
 Comic Sans walks into a bar and the bartender says, 'We don't serve your type here. 
More on typefaces