They are very handy for bettering yourself, primarily as a way to notice things that you would have missed otherwise. A parser isn't going to help you find a better rotation or press buttons more efficiently, but it sure as heck gives you a number you can use to see if you're doing better than average or not.
Here's my anecdote to provide an example: I reached level 80 RDM and started running the 3 level 80 dungeons in a blend of i430 and i440 gear. I know my rotation and am used to being at or near the top of dps in all prior content I've run but noticed that while my DPS had gone up it didn't compare to the other level 80 people that I was running with by a large margin. I expected to be on the lower end of things due to just getting into the content, but these people were suddenly and very unexpectedly doing more than 40% more DPS than I was. At first, I just assumed it was my ilevel since many people were running i450 gear by then, but I was a bit suspicious that such a dps difference would be due to only 10 ilevels. This suspicion was further increased when I noticed after a few runs that some people in mixes of i430 and i440 gear were also outperforming me by several thousand dps and I was only 1-2k above the tanks in output. I knew I wasn't doing anything wrong at all in terms of rotation, so I was confused. I decided I would try melding to see if that would help even though I wasn't in the end-game gear yet. I didn't even overmeld and the difference was both huge and instantaneous. I gained a 40% increase in my DPS output on the very next run, and would have been completely clueless that I wasn't performing as well as I could have without the parses. Yes, I knew melding would increase my output, but I had just assumed I didn't need to bother until I got into the i450 gear since the general consensus is that it isn't that big of a difference and only really has an impact in savage. Parsing let me see how wrong that assumption was, and led to a huge improvement in my performance. If I hadn't had access to a dps parse, I would still be sitting here happily pumping out only 8-9k dps in level 80 dungeons instead of the 12-13k I can manage now and thinking I was doing well.