Are all wheels compatible with all cars as long as the tire size is the same?
 

I was planning on going to a salvage yard to look for wheels for a 95 Honda Civic. The tire size is 175/65 R14. So if I see this tire on another car that isn't a 95 Honda Civic and happens to be a Dodge Neon for example, would the wheels from the Neon be compatible with the Civic? Or should I search specifically for other Honda Civic wheels with this tire size?

You need to ensure that the bolt pattern is the same as well as the proper back spacing. There are cars that share the same bolt pattern but you need to do cross check.
Your wheels are probably 14X5.5 4-100 114 35
This link explains what the numbers mean

Understanding the Wheel Size - Discount Tire

You didn't say what year and style the Neon was but a 2000 base model with 14" wheels would be 14X5.5 5-100 11435

If so they would not fit as your car has 4 lugs and the Neon has 5.

^^That.

hub bore/diameter plays a role as well. Some Mazda miata wheels are 4x100, but they have a smaller hub size or something. i believe hondas are 57.1. Google it to be 100% though.

also be aware that tires have a shelf life of 6-10 years make sure you check the manufacturing date.
The Safety Report » Tire Safety