A lot of the examples in this article are kind of gimmicky. MailChimp, for example. You would be better off ignoring the chimp, who usually links to YouTube time-wasters as if they were important messages (the chimp is usually the "visually loudest" item on the page). Personality? Yes. But maybe not a good inspiration for your own product's personality. Maybe too much trading-off of utility.

To me, the web product that had the best personality of any is Feedburner. Kind of funny, creative, and slightly self-deprecating in consistent ways (e.g.: "troubleshootize" offsets the selling-out nature of "monetize"). The same clever, helpful, friendly voice is present on every page without getting in your way. The jokes are still actually, clearly communicating content. A tremendous achievement, IMO, and I believe it has kept me loyal despite their Google acquisition.

Groupon's email "personality" has attracted a lot of praise, but it’s polarizing, and I cannot stand it.

Another positive example is Pandora. The interactive, conversational tone encountered when setting up a station -- this was back in, what, 2005 -- has been a personal inspiration to me.

A counter-example is Stack Overflow, IMO. All the "site" messaging feels off to me. I’m always unceremoniously and orange-ly invited to "Read the FAQ." Told I can do something, and then prevented from doing so for having violated a secret policy, with a note that puts the blame on me ("Oops, edits need to be 6 characters or greater!"). Told I have "been logged in" and that I should click to refresh the page. It’s a personality, but it’s not a friendly one. It’s a red-tape-with-a-technical-explanation-from-a-lazy-programmer-with-no-UX-concept personality. An anti-pattern in site personality.

Be like Feedburner!