(...) typically with a direct connection to the database <-- I guess you are thinking about DataProviders in ASP.NET, huh? Yeah, they tend to disorganize the development. Either you use them everywhere, or you don't use them at all.
Quora is event driven and huge. Friendfeed acquired by Facebook (Cofounder Brett Taylor is now Facebook's CTO) was based on an event driven architecture. LinkedIn Mobile I believe works with node. I don't think event driven web programming is for small sites. I think it depends more on whether your site/application is extremely dynamic independent of user interaction.