MOSFETs are too noisy for many precision amplifier applications. If you have a low impedance source, for the lowest noise of any available monolithic amplifier, you need to go to a bipolar amplifier such as the LT1028 which has a white noise spectral density of 1.1nV/sqrt(Hz). (If that's not good enough, a discrete design can do better).
Contrast that with a typical MOSFET-input amplifier such as the MCP601, which is typically 29nV/sqrt(Hz), or about 700 times worse in terms of power.
If you are doing audiophile audio processing, the best amplifier in the world is a Texas Instruments (nee Burr-Brown) bipolar part. It has a lot of input bias current, but very little distortion.
MOSFET amplfiers also seldom are capable of working with higher supply voltages, such as +/-15V (another frequent requirement of precision instrumentation), and if they are, they tend to cost an arm and a leg, I think that's mostly because they have to be made on a special high-voltage CMOS process line and not mixed with digital stuff.
The 741 was designed in the mid-1960s, so almost 50 years ago. It was somewhat of an improvement over even earlier op-amps (such as the uA709), but it's pretty long in the tooth. Dual versions such as the venerable JRC 4558 have been used in audio applications for decades. As Olin points out, the LM324 is similar (the output stage has significant differences, in part to make it "single supply"), but costs only a penny or two per amplifier in quantity.
Aside from the LM324, I don't think any other op-amp has achieved as wide use as the 741 (maybe some of the JFET amplifiers come close)- the market is more balkanized, with many different choices for the designer, each with its own advantages and disadvantages. Vive la différence!