In my asp.net applications, I've typically used the Application_Error global event handler to log the error and redirect the user to a user-friendly error page.
However, I have read about ELMAH and while that seems interesting, Application_Error seems like the simpler approach.
I've read other questions where people, including myself, have suggested one way or the other. What I'm wondering is if there is any significant benefit to using one over the other and why?
Elmah is a fantastic project and we use it for all of our ASP.NET applications. Not only does it log unhandled errors for you, it grabs the entire original page that the user saw, which contains a lot of detail for you.
It has email support, RSS feeds (both itemized and digest) and has an attractive console.
For 3 lines in config and a dll reference, I'd say that's a slam dunk.
I guess the main drawback of ELMAH is that it might be overkill for what you need. If it's logging and storing more info than you would in your own implementation, that's an unnecessary overhead in storage and processing. You also need to think about how you secure access to ELMAH's console since those exception details could contain juicy details of your app (that needn't be hard, but it's a worry that you didn't have before).
On the other hand, your own implementation will probably grow to log all that extra information once you decide that some stubborn bug requires it, and do you really care about shaving fractions of a second off the time that it takes for the error page to be displayed? Chances are you'll eventually end up building your own version of ELMAH, so why not just use ELMAH and save yourself the time.
I'd recommend that if you do want to write your own error logging rather than using ELMAH, you at least put it in a module rather than straight into Application_Error in global.asax. Just subscribe to the application's Error event in your module's Init method, and you can easily reuse your error handling code in another application with a line in web.config.
I also find it useful to handle any exception logging through ASP.NET's health monitoring. This makes it easy to control the type and level of logging in web.config, and also allows logging of exceptions that were handled in a try...catch without getting as far as Application_Error. Create a custom HandledExceptionEvent class that extends WebRequestErrorEvent, and you can create and raise those events in any catch block where you'd really like to know that the exception happened even though it was handled.