What is the best way to monitor PHP functions/executions?

I am trying to find the best way to monitor which PHP code/functions, MySQL requests and/or plugins are slowing down pages on a site.

I know there are a bunch of different options out there including wordpress plugins and solutions involving firebug (firephp) but what do you guys feel is the best approach?

Personally I feel the ideal solution would be to have some type of code which can be installed by default with every wordpress install. Any debugging/monitoring/reporting would ONLY get executed if you added an optional entry to the end of the URL like ?=debug. For security purposes it would be even better if one would first have to login to the wordpress admin area and create a temp debug key which would create a hashed key and append it to the url (like debugkey=v09098v09aq2ov1a8923) which would only be available for 30 minutes.

But getting back to the actual debug info… I feel using firebug is great in many situations but optionally I feel it would be valuable if one could append something else to any URL which would for example overlay all the functions, hooks or filters used on a specific page along with the execution time for each.

In any case… I figured many of you here must have faced this issues as well and thus I would appreciate whatever solutions you are utilizing to solve your problems.

Please do outline how any specifics for others that might read this describing any specifics on installation and how to use it correctly.

UPDATED
Running a Dedicated Linux Server

There are multiple tools and possibilities, and shure it would be nice to have something quick at hand. I know plugin authors who do offer debug flags so you can analyze what’s going on quite easy.

As for plugins, I have not tested it but looked at some screenshots and it is at least informative: Debug Bar (WordPress Plugin) and the BlackBox Debug Bar (WordPress Plugin).

Another one is a hooktracer that is not that well known: SJ Hook Profiler.

I do heavily recommend xdebug for development and testing systems, it’s a pleasure to have it if you need to profile or debug stuff.