In the comic book industry, changes to an established superhero's costume are usually avoided because a character's costume is vital to its recall value among readers. Drastic changes can result in alienating readers and could mess up merchandising campaigns (something as simple as changing a superhero's costume from red to blue could result in thousands of products with the red-colored version of the character instantly outdated and irrelevant). This is the reason why it took several decades before they finally managed to get Superman out of his briefs, and why The Silver Surfer is still a bald, chrome-painted dude wearing nothing but a surfboard.
However, there are exceptions. There are haracters who had costume changes or alternate costumes that added more to the franchise and were embraced by the fans themselves. Such as:
Tony Stark's Numerous Variations of the Iron Man Armor
The Iron Man franchise had the advantage of design changes and armor upgrades being an integral part of the story. Tony Stark has gone through dozens of costumes, starting from a silver-themed, bulky armor with a bucket for a head, to a gold version, to the more modern version you see on the movies. They got away with it by establishing not the look, but the color scheme of the character - red and gold. Over time, they've managed to shed even that and pin the franchise more on the person behind the suit and his ability to pull random variations of the armor out of his arse.
Jean Paul Valley's Armored Batman
This isn't really Bruce Wayne's alternate costume, but his temporary replacement, Jean Paul Valley's. When Jean Paul Valley first took over the role of Batman (after Bane broke his predecessor's back), he used the conventional Bat and Cowl costume but promptly got his posterior whooped by the stronger, faster, and 'roided (venomed. actually) Bane. Valley then decided to change the cape and cowl with a new costume that looks more like a suit of armor than tights and spandex. Armed with flamethrowers, mini-batarangs, and sharp claws, Jean Paul Valley managed to do what Bruce couldn't: send Bane to the hospital.
Spider-Man's Black Symbiote Suit
Spider-man's red and blue costume is iconic, and has remained consistent for a long time (with differences being exclusive to minor changes in the size of the eyes), so it was an impressive feat that the black symbiote suit managed to gain a lot of fans. Perhaps because there was a decent backstory to the new costume instead of something that writers pulled out of their hinds, or maybe it's because the black costume actually gave him cooler powers. The suit is gone now, having moved to a different host, but it continues to make appearance in various media (especially in the Spider-Man videogames).
Personally, I think the jumpsuit-wearing Hulk, which appeared around the time when Banner and the Hulk persona become one, looked goofy. But I consider it a great improvement over what Hulk's been wearing for the past few decades: a pair of torn slacks that magically stretch several sizes larger, and always rips at the lower part, never at the groin area.
Everything that Luke Cage Wore After He Dropped the Power Man Costume
The Power Man costume is a tight-fitting, yellow long-sleeved shirt with a collar and a plunging neckline that will make Lady Gaga blush, punctuated by a tiara over his Afro. There is no need to explain why the new costumes are considered as a great improvement.