How do you log errors (Exceptions) in your ASP.NET apps?
I use elmah. It has some really nice features and here is a CodeProject article on it. I think the StackOverflow team uses elmah also!
I've been using Log4net, configured to email details of fatal errors. It's also set up to log everything to a log file, which is invaluable when trying to debug problems. The other benefit is that if that standard functionality doesn't do what you want it to, it's fairly easy to write a custom appender which can process the logging information as required.
Having said that, I'm using this in tandem with a custom error handler which sends out a html email with a bit more information than is included in the standard log4net emails - page, session variables, cookies, http server variables, etc.
These are both wired up in the Application_OnError event, where the exception is logged as a fatal exception in log4net (which then causes it to be emailed to a specified email address), and also handled using the custom error handler.
First heard about Elmah from the Coding Horror blog entry, Crash Responsibly, and although it looks promising I'm yet to implement it any projects.
I've been using the Enterprise Library's Logging objects. It allows you to have different types of logging (flat file, e-mail, and/or database). It's pretty customizable and has a pretty good interface for updating your web.config for the configuration of the logging. Usually I call my logging from the On Error in the Global.asax.