The 555 is a common IC. It can be used as timer, timer delay, for pulse generation, oscillator applications, as a flip-flop element.
It is a special type of amplifier circuit used since 1968. It is also common. 741 requires both positive and negative supply rails.
Essentially similar like that of 741. It does not need duel rails.
The 4017 is decade counter, for counting pulses.
Motor Driver, H-bridge motor driver etc.
It is comparator. It compares two voltages and switches digital output to indicate which is larger. LM339 is same but LM393 has two comparators inside.
7805, 78XX Family
Simple voltage regulators as IC. They accept an input voltage and produces an output voltage of constant value.
7805 produces a 5 V output. Input voltage can be 9V to 35 V.
NE5532 and LM324
NE5532 is a good quality amplifier which can be used in both AC and DC circuits. It has 2 amplifiers inside.
LM324 is similar but has 4 amplifiers inside it.
It is also amplifier IC. It has one amplifier inside and suitable for medium audio output from a speaker, buzzer etc.
This IC commonly used to drive large LEDs, small stepper motors, relay coils. It has 7 identical circuits inside it.
It is digital IC. it is a 6 channel inverting Schmitt trigger.
Common use is as port expander, normally to increase the number of digital i/o pins of Arduino.