They are, designing fonts can be fun and ultimately they can have a huge effect on the message that you are trying to convey.   They do matter, just don’t select a font and hope for the best – the subject of your site is crucial.  For example don’t pick a flowery, artistic font for a site which deals with science or mathematics for example- it will just look stupid.

Check out the amount of text that will be on a page, lots of text will need clearer, less fussy fonts which are easier to read.   If you site contains lots of video and pictures, you can then use something a bit more interesting and artistic.