I remain a huge fan of log4net, and it remains my favorite tool for logging.
Sometimes you might not have time to use it, you may be at a client who doesn't use it, or its not available to you for any other reason.
You could certainly use the built in logging functionality in Sharepoint, outlined here. Another possibility is to use the .net (System.Diagnostics) built in Trace functionality in combination with the freeware SysInternals tool DebugView.
Start it up, and watch as your Trace messages fly by.
Your assembly must be compiled with the Conditional Compilation Constant Trace defined. This is standard in the DEBUG mode for Visual Studio.
This is great for debugging and testing, and should never be used in production for obvious reasons.
I use the Trace functionality at times in combination with log4net to report any error that the log4net library might have during configuration.