Would like clarification

Looking to purchase some new outlets, I've heard folks say that you can't use 15 Amp power cables in 20 Amp outlets,
it looks like the 20 Amp outlets I commonly see will accept a standard 15 Amp power cable plug. Why not?
20 amp outlets accept 15 or 20 amp cords.  20 amp IEC (component end) is different than 15 amp IEC and are not interchangeable. 
The rule is if they fit together they can be used together. Remember that one simple rule it works with everything.
@bobspets1 - Yes - they fit but - here’s the problem - if you put a 20 amp outlet in place of a 15 amp outlet you are contravening the electrical codes.-

- because - now you can now plug a 20 amp device into that outlet
- and unless the wiring is also upgraded to 20 amp - it contravenes code
- SHORT STORY - it is a very real fire risk
- the insurance company would deny any claims

If you want to buy a better outlet then look for a Hospital Grade or MRI grade outlet - they clamp down on the plug for a better connection

e.g. - Hubbell 8200HW Hospital Grade Outlet Cryo Treated - Hubbell Cryo Treated 15A/20A Wall Outlets - (takefiveaudio.com)

I have used these for years as wall utlets and in my power distribution box and they work extremely well.

Regards - Steve
First off, you can plug 15A power cords into 20A circuits.  If you try to draw more than 15A, which you can from a 20A circuit, with a 15A cord, you will have a problem.  If you draw less than 15A, you're OK.  Most newer houses run 20A circuits (12AWG) for electrical outlets.  Building codes let builders use 15A outlets unless it's the only outlet on the circuit.  Builders use the 15A outlets because they are cheaper.

Before you replace an outlet, you need to turn off the circuit breaker to that outlet.  If it's a 20A breaker, you can use a 20A outlet.  Also, the wire should be 12 AWG.  If it's a 15A breaker(usually used for overhead lighting), you can only use a 15A outlet.  The wire then would be only 14AWG.
Looking to purchase some new outlets, I've heard folks say that you can't use 15 Amp power cables in 20 Amp outlets,

If you mean the 120V, 20A outlets with the T shaped prong receptacle on one side, it is perfectly safe and legal.  Here is an example:


What you may not do is put one of those 20A receptacles on a 15A circuit.

What you also have to worry about is making sure you have the right gauge IEC cable for the device you are connecting it to.