There are two important things to realize with Damage Meters though:
1. The HPS or total healing of a healer is not necessarily relevant to her worth to the raid.
2. The DPS or total damage of a damage dealer is not necessarily relevant to her worth to the raid either. Even if it is much more so than healing is for a healer.
Once one accepts this, they can be an interesting tool. Certain small shifts in setup or buff spreading can have outstanding effects on total raid DPS - we pushed nearly 20k extra raid-DPS on Lanathel25 by resorting positioning to optimize bite-travel-time and totem coverage, and it was interesting to see how some people lost minor amounts of DPS, others gained some, and in total we fielded 20k more (and killed her! \o/).
As said already Death logs are very interesting, even if both Recount and Skada have fairly bad ones. Acherons are awesome but I think the mod is no longer updated.
Failmeters can be good if you suspect your group is doing something wrong at a base level, check how many got hit by what fire how often and see whether positioning is just screwy.
Lastly, while the meters themselves are fairly useless for judging people (meaning don't look at people in comparison to each other unless you know what you're doing!), isolated per-player stats are very interesting. Composition of healing and damage tells you whether they do something clever or wrong, and total numbers can tell you whether they slack or miss crucial utility to perform.
But as said, nether DPS nor HPS reflects the worth of a player to the raid. It's a part of it, but not as large a part as people would like others to believe. That is, the people who are top and frantically spamming their meters would love you to believe it is their worth, but it only goes to show they got nothing else to lean on.
-- (The Death of Rats, Terry Pratchett, Soul Music)