Not the op-amps. Whole amplifier circuits. Three different circuits using the same op-amp can sound different because they are different. If you change the op-amp of one of these circuits then you can get another different circuit with another different sound signature. It's not because the op-amp sounds different; it's because it's electrically different and the circuit isn't being adjusted to match those differences.
Now for an important fact: two op-amps of the same type, the same manufacture, side by side in the same production batch, can have different electrical characteristics. This is where more expensive op-amps become useful in audio equipment. A higher quality op-amp doesn't sound better than a cheap op-amp but it is manufactured and tested to stricter tolerances. This makes for less variance when a given op-amp is used in manufacture. Less variance makes for fewer or no noticeable differences across an entire production run of a given mass-produced amplifier circuit. It makes for less work matching components in hand-made amplifiers.
Turning the whole thing around, if a given op-amp had a distinctive sound signature then the circuit wouldn't matter. A given op-amp would sound exactly the same in a $50 cMoy amp as it would in a $6000 Cavalli Liquid Gold amp. I don't think I need to write anything about how absurd that idea is.
Edit: if you're still with me and still curious then I suggest checking out a book on basic electronics from your local library. Any decent electronics book should have a section on amplifiers and should be better than I at explaining exactly how amplifiers work.
Edited by ratinox - 1/31/14 at 4:14pm