A person who participates in weightlifting, is a person who squats, cleans or snatches at least once a week and this article is devoted to you.

1-Shoes aren’t created equal 
It is important to understand that different shoes have different purposes. In weightlifting, you need shoes that are going to help you use all the force that your body will produce. Running shoes are designed to absorb impact and you can bet that they are going to absorb some of the force that you put into the ground .This absorption will likely cause your body to compensate. It is not uncommon to have sore knees and a sore back after lifting with running shoes.
2-The shoes can help increase your squat ,clean and snatch
Weightlifting shoes are designed to help you channel the force you produce into the ground. The more force you produce into the ground, the more weight you can move!
3-Weightlifting shoes usually have a raised heel of about half an inch or more 
The raised heel actually increases your ankle’s range of motion. An increased range of motion means you will find yourself in a deeper squat position. A deeper squat position allows for more upright posture and an increase in muscular activation. The heel allows for improved performance and also decreases the risk of injury!
4-You want the shoes to be snug 
Runners and other various athletes prefer to have a little leeway in their shoes. Weightlifting shoes have to be snug. The last thing you want is for your foot to be sliding around in your shoe, when you are trying to squat or clean.
5- Good weightlifting shoes aren’t cheap 
The cheapest quality weightlifting shoes start at $80 and some pairs can run upwards of over $250. I like to tell people to be committed to weightlifting before investing in a good pair of shoes

If you don’t actively “weightlift”, I would look into your exercise program and determine if you are using the right kind of shoes

Nader’s Recommendations for shoes :
Adidas adiPower
Rogue Do Win