There are many third-party applications out there that enable this sort of functionality. You will pretty much need to choose between a log monitoring / consolidation product and an alternative event log reader on steroids (one that queries multiple servers without the need to connect to each and every one of them).
The former has the advantage of usually supporting enhanced features such as notifying you via email when events occur, enhanced reporting (e.g. statistics) as well as long-term archival. Since those products also store the events in their database, you are also insulated against connectivity issues between the local and the remote machines. Our product EventSentry offers such functionality (and much more if desired). Disclaimer: I work NETIKUS.NET ltd.
The latter (I have not evaluated any of these products, but I am speaking of experiences from reviews, screenshots, etc) are probably quicker to setup and cheaper - but with limited functionality.
Regardless of the solution you pick, I recommend against manually reviewing logs. It's a tedious and passive process. Instead notification is really the only way to reliably fix problems as soon as they occur. Plus, general health of your web servers should be monitored as well (disk space, performance, service availability, etc.).
Hope this helps.