This answer attempts to roughly describe 741 for beginners and why this ancient beauty should be laid to rest forever.
EDIT : Added : This answer also applies to the LM358 opamp
Key Words (for searchers) : output too low , output won’t go to zero , output won’t go to 0, Use 5 volts , single ended , single power supply , do I need negative power supply , Vee is zero , Vee is 0 , Vee is grounded , LM358
741 op amp : Born 1968 (with limited improvements throughout its career).
What are limitations of the 741
This answer attempts to roughly describe 741 for beginners and why this ancient beauty should be retired after a long and distinguished career.
Data sheet for 741 : 741 Op-amp
Range of output voltage (2 K ohm load) : The Guaranteed swing, for a supply of +15 and -15, the output can only go up to +10 volts and down to -10 volts. Typical is listed as output +13 to -13 volts.
Range of output voltage (Load >10K) : The Guaranteed swing, for a supply of +15 and -15, the output can only go up to +12 volts and down to -12 volts. Typical is listed as output +14 to -14 volts.
This means that, for any given supply voltage, the output can only get within a few (1 to 5 volts) volts of Vcc and Vee (commonly called “the rails” depending upon load.
Example : Let Vcc= 7 volts, Vee= -7volts. Output could go up to +2 volts and down to -2 volts (worst case). If Not worst case : possibly output up to 5 volts and down to -5 volts. Don't even try to use the 741 with a single 5 volt power supply.
Using single supply (with or without virtual ground) : Suppose +15 volts is used for Vcc, and Vee = ground. Output could go up to 10 volts and only as low as 5 volts (worst case). You might get the 741 to go as low as 2 volts, but not lower. Output can never get close to 0 volts (ground).
Current technology (and inexpensive) has what is caled “rail to rail output”. This means the output can approach the rails (Vcc and Vee) even with single ended supply (Vee connected to ground).
Input offset voltage : Specified as 6 mV worst case. Without nulling offset voltage or other means of correction, this means 0.006 ( 6 mV) will be amplified by the gain of your amplifier and will appear on the output. So if you want a gain 0f 50, you end up with 0.3 volts error on your output signal.
Current technology (and inexpensive) has offset voltages of well below 2 micro-volts. Reduce your errors by a factor of 1000.
Input Offset Current : Typical for 741 is 20 nA (that is nano-amps). Current technology (and inexpensive) has offset currents in the pA (pico-amp) range. Reduce errors due to offset by greater than a 1000. Input offset current becomes very important in high impedance circuits.
Input Voltage Range : For Vcc =15 and Vee = -15 this is specified at inputs must be less than +/- 12 volts. Don’t expect the circuit to work if inputs get within 3 volts of the rails.
Large Signal Voltage Gain : Typical specification is 200,000. This sounds like a wonderfully high gain. But it is not. This is actually quite a low gain for op-amp. Current technoloty (and inexpensive) have gains well in excess of 1,000,000. High open loop gain is important for many reasons (far beyond this answers intent). For amplifying DC, the 741 gain might be ok. For amplifying AC signals, you should seek more than a 200K gain.
Slew Rate : Specified at 0.5 volts per micro-second. This means that the output could rise by 5 volts in 10 micro-seconds. That is pretty slow if you expect anything more than audio frequencies.
Replacements for 741 : Commentors suggested MCP6001, TLC271. For single ended supplies, the TLV2462CP is a good candidate. You can go to various suppliers websites and search for what parameters are important to your project.
The 741 deserves a nice retirement. Let this device enjoy its retirement. Give a big round of applause for a job well done for many many years.