There was a time when there were only half a dozen typefaces (fonts) which could be used on a website. Other than the logo at the top, which would be a graphic image, there was no way of matching your website with your corporate style (and I believe that even the smallest company should have a simple corporate style).
Now, however, there are many more fonts which can be used on websites, such as Google Fonts and Adobe Edge Web Fonts. These have been a major factor in why many consumer-facing websites are looking so much better nowadays than the average, rarely-redesigned, B2B site.
Despite the number of fonts available, it’s still unlikely that you’ll be able to match those which you like using in print. If that’s the case, then next time you give the website a refresh, why not consider changing your corporate style (or even defining one for the first time)? If you can find one or two acceptable fonts which are available (1) as web fonts, (2) as desktop fonts for correspondence, and (3) as high-quality fonts for literature, then you might be able to start producing some stylish – and consistent – corporate communications.
(Apologies for wasting your time if you work at a large multinational where the 150-page corporate stylebook is issued from the other side of the world every 10 years)