Used introspectively, combat log add-ons have some value. They also have some limited application in analyzing a raid group, if used judiciously and tactfully, at the discretion of the raid leader.
So let's start how NOT to use these tools:
[Guild] (Àrthás): fail pug ful of bads so trd of caryng nbs
[Guild] (Àrthás): Recount - DPS for Overall Data
[Guild] (Àrthás): 1. Àrthás 35425.2 (35.2%)
[Guild] (Àrthás): 2. Stabby 29688.7 (29.5%)
[Guild] (Àrthás): 3. RCain 19725.4 (19.6%)
[Guild] (Àrthás): 4. Îńsæńity 13586.4 (13.5%)
[Guild] (Àrthás): 5. SirHealsaLot 2214.1 (2.2%)
[Guild] (Àrthás): xD
What's wrong with the above example? First and foremost, it's posted in guild chat. I hear that's a no no.
So since I can't post my numbers in guild chat, what good is this thing? Well, the interesting data isn't found in overall dps, and dps on a the boss rarely tells the whole story. It's definitely not found in comparing the dps of an affliction warlock (currently the highest dps in the game) to that of an arms warrior (currently the lowest dps in the game). It's a bit more complicated than that.
Most fights have a target prioritization. Target boss, when adds come out, kill the adds, get back on boss kinda thing. Okay, so how am I doing here? That can be interesting.
A lot of fights have avoidable damage. By not standing in the fire, the healers have better mana resources to heal you up when you are taking damage that can't be avoided. Combat log add-ons can give you an idea how well you're reacting to things.
Some encounters offer opportunities to greatly improve your performance through special buffs. These may or may not be spread evenly or available to all party members. As one example, in the Gara'jal encounter, when you enter the spirit world and you are healed, you gain a buff called Spiritual Innervation. It's unique to each class, but basically improves your performance. These buffs can also account for disparity between dps on any given encounter.
Friendly fire can also be interesting. Now, not all friendly fire is avoidable, not all friendly fire is bad. (In most cases it is) Am I staying away from the group when I have a debuff that not only damages me, but damages anyone around me? Arcane Resonance, hello.
All of this really oversimplifies where the real interesting information lies for each encounter, because it really is so scenario-specific to each encounter.
None of this is to say that DPS (e) is meaningless. It's critically important, within the context of all the other things that are important.
Perhaps the most valuable application of any combat log add-on is comparing performance between two players of the same class and similar gear levels, especially when the other player has better numbers, and referencing this against their spell usage and talents. Wow, that other talent option really performs better for this encounter.
If you're into the numbers thing, include other measures of performance along with effective dps. Good raid performance is multi-dimensional.