There are a lot of situations where people record themselves. I've seen people who are trying to improve their golf game that haul their video recorder out to the driving range and set it up to record themselves so they can analyze their swing. Professional speakers record their speeches and play them back to hear how the speech will sound. And, musicians record themselves to hear how their performance and practice sounds.
There is a lot of different equipment you can buy and use to record with. One thing you should keep in mind though is that you really don't have to spend an arm and a leg to this. I do have a little home studio recording rig I use with my laptop to record my playing and practicing with but, you can accomplish the same basic idea of this whole thing by getting a hand held digital recorder for less than 50 bucks. If I remember right I picked one up at Radio Shack for $35 that I use most of the time. It's simple and easy to use and take virtually no time to turn on and get started. If you want to go real cheep you can buy an adapter for the plug on your instrument cable and plug it right into your PC, you can then record to your computer for about $5.
I remember the first time I recorded myself practicing, it was almost shocking. I thought that I was tearing things up, and it wasn't really too bad, but when I recorded it and listened to it. I was bummed. It sounded terrible, but the bright side was that it really opened my ears up to what I needed to work on for technique. It let me hear my amp and effects so I could make some adjustments. It let me hear my voice too, which prompted me change the key of a song that I was practicing to better match my voice.
There's no better way to critque yourself and improve than recording your practice sessions. You will hear yourself in a new light by being able to actually hear what you are performing or practicing.