In the past, I've mostly used LF 347 for multipole filters and stuff requiring several stages.
Old Depot discussions are gone, where we covered qualities of the various single, dual and quad opamps, like LF347, TL084, the Burr Brown's and the Analog Devices.
Now, I'm not really thinking about which is the best, but more about which are good candidates for which applications.
So, things like types of filters with how many +- dB, low-gain and unity gain buffers, hi-gain applications like with compressors and distortion stomps, needed open loop gain, stability and compensation needs, noise figures, ability to gracefully handle overload, how tone might be affected in good or less good ways, like JFET inputs, MOS types, bipolar designs..
I'll hit a few opamps and applications as I see it:
Signetics NE 5532/34's: Good for keeping clarity, when higher gains are needed without changing tone. Less of a 'guitar' tone, as those are quite transparent.
CA 30xx CMOS: Can add a touch of soft tone, useful for unity/low gain. Handles some overload gracefully. Not good for higher gain applications.
Various AD and Burr's featuring JFET inputs: Handles overload gracefully. Good for higher gain applications.
LF 347: An overall good workhorse. But is it good for demanding higher gains in complicated filters?
TL 084: Same as LF 347; tone seems a little different, but how to explain?
Old-school TL 54xx types: Not generally too interesting, but can have an interesting way of distorting when overloaded.