This is tagged with the marvel-cinematic-universe tag, so I'm going to answer from that perspective.
In roughly the order we were introduced to them;
- Tony Stark, AKA Iron Man. He created his first Iron Man suit when in captivity in Afghanistan. Since then, he has upgraded and tweaked the suit many, many times.
- Bruce Banner, AKA The Hulk. He has no costume.
- Natasha Romanoff, AKA Black Widow. Her costume would have been provided by SHIELD, her employer throughout most films she appears in so far.
- James 'Rhodey' Rhodes, AKA War Machine. His costume was designed by Tony Stark before being stolen and further modified by the US Army.
- Thor Odinson. Although what he wears may looks strange to us, it is actually just standard Asgardian armour, possibly somewhat fancier than usual thanks to his status as Prince of Asgard.
- Clint Barton, AKA Hawkeye. Like Natasha Romanoff, his suit and equipment would have been provided by SHIELD.
- Steve Rogers, AKA Captain America. His first costume was designed for him as part of a propaganda campaign, before being upgraded by Howard Stark in order for him to take an active role in the Second World War. Since then, he has had a costume designed by SHIELD Agent Phil Coulson, before being employed by SHIELD and later joining The Avengers full time.
- James Buchanan 'Bucky' Barnes, AKA The Winter Soldier. Other than the standard military style gear he wears, his equipment and robotic arm were created by Hydra.
- Sam Wilson, AKA The Falcon. Another member of the Avengers, and again we don't know if his identity really is a secret or not. His costume is the EXO-7 Falcon, a piece of military equipment that he stole.
- Pietro Maximoff, AKA Quicksilver. We never really see Pietro in anything that could be described as a costume.
- Wanda Maximoff, AKA The Scarlet Witch. We have not yet seen Wanda in anything that could be described as a costume.
- The Vision. He looks pretty weird by default, but we do see him create a cape for himself based on the one that Thor wears.
- Scott Lang, AKA Ant-Man. His status as of the end of Ant-Man seems to indicate that he does keep his identity secret from everyone other than his close friends and his family. His costume was created by Hank Pym, a scientist who previously used the Ant-Man suit to fight for SHIELD some decades ago.
- Hope van Dyne, AKA The Wasp. Although we haven't seen her use it yet, her costume was created by Hank Pym and his wife, and has now been handed down to her.
Agents of SHIELD
- Mike Peterson, AKA Deathlok. His "costume" is a series of cybernetic enhancements created by Cybertek in association with Hydra.
- Daisy Johnson, AKA Skye, AKA Tremors. Her gauntlets were designed by Agent Jemma Simmons. Presumably, her suit was also provided by SHIELD after she set up her Secret Warriors team.
- Lincoln Campbell, AKA Sparkplug. Like Daisy, his suit will have been created and provided by SHIELD when he joined the Secret Warriors.
- Joey Gutierrez. As a member of Secret Warriors, he too was given a suit by SHIELD.
- Matthew Murdock, AKA Daredevil. His costume was created by Melvin Potter, a tailor who creates special protective suits for Wilson Fisk and his associates.
- Jessica Jones. She did have a costume that was created by her friend Trish Walker, but as far as we know her career as a superhero was both short lived and didn't actually include her wearing the costume.
- Luke Cage. So far in the Marvel Cinematic Universe, we have not seen him wear anything that could be described as a superhero costume.