Reasons not to use a 741 op-amp?
There are many good reasons not to use the 1968-vintage LM741: -


Minimum recommended power supply rails are +/- 10 volts


Modern op-amps have power supplies that can be as low as 1.8 volts.

Input voltage range is typically from -Vs + 2 volt to +Vs - 2 volt


Modern op-amps can be chosen that are rail-to-rail

Input offset voltage is typically 1 mV (5 mV maximum)


Modern op-amps can easily be as low as a few micro volts and have low drift.

Input offset current is typically 20 nA (200 nA maximum)


Modern op-amps are commonly available that are less than 100 pA

Input bias current is typically 80 nA (500 nA maximum)


Modern op-amps are commonly less than 1 nA

Input resistance is typically 2 MΩ (300 kΩ minimum)


Modern input resistance starts at hundreds of MΩ

Typical output voltage swing is -Vs + 1 volt to +Vs - 1 volt


Many cheap rail-to-rail op-amps get to their supplies within a few mV

Guaranteed output voltage swing is -Vs + 3 volt to +Vs - 3 volt
Supply current is typically 1.7 mA (2.8 mA maximum)


Modern op-amps with this current consumption are ten times faster and better in many other ways too.

Noise is 60 nV/sqrt(Hz) for LM348 (quad version of 741)
GBWP is 1 MHz with a slew rate of 0.5 V/us


The LM741A is slightly better but still a dinosaur in most areas.

Things of importance that the 741 data sheet does not appear to list (and that may depend on the age and manufacturer): -


Input offset voltage drift versus temperature
Input offset current drift versus temperature
Common mode rejection ratio versus frequency
Output resistance (closed or open loop)
Phase margin
likeliness of latchup (and gain reversal)


I can't think of any valid reasons to use the 741 other than "that's all I will ever have or own". Common reasons why they are still used in actual devices appear to be: - 


Someone had a design that they didn't want to change from the 70s
Someone had millions of them lying around and wanted to put them to use
Someone actually determined that all the parameters are fine for their design, and at that moment the 741 was the cheapest to acquire and in millions of units it saved a few thousand dollars in total.


I've been an electronics designer since 1980 and I have never used or specified a 741 in any design I've been associated with. Maybe I'm missing out on something?