Kingdom Come addresses this in the novelization. Heroes are impoverished and uncontrollable, so there's no way to deal with the destruction superheroes cause. No one owns automobiles due to the skyrocketing insurance, and public monuments tend to be left where they lie.
A Superboy series begins with the wide-spread destruction of Smallville and the surrounding farms due to the titular character's battle with Parasite. Superboy recognizes that this might very well spell doom for the entire town, as the collapse of the area farms will lead to massive unemployment, work migration and bankruptcy, so he arranges the first ever Superboy vs. Kid Flash Race to raise money for repairs.
Supergirl: Supergirl usually tries to cleans up after her violent battles:
In Supergirl (2005) #12, new hero Atlee helps Supergirl take out a giant dinosaur; after the battle she uses her earth powers to repair the streets and even fix a fire hydrant. It is later revealed in the Terra miniseries that she apparently does this after every battle.
In Red Daughter of Krypton, a city gets leveled and burned down because of a battle between two groups of Red Lanterns. Supergirl and her Red Lantern team want to help out with rebuilding it after the battle, but the frightened locals beg them to leave as soon as possible.
Bizarrogirl provides several examples: Kara accidentally blasts her bedroom's ceiling, so she fetches a paintbrush and a paint bucket and sets out to repair the damaged surface. Meanwhile, the Justice League is helping out with rebuilding efforts after the "New Krypton War".
Newscaster: Across the planet, the Justice League has led reconstruction efforts at sites hit heaviest by the Kryptonians — including Cairo, Paris, and Metropolis.
In one The Supergirl from Krypton (2004), Smallville is trashed in a superfight at the climax. The next storyline begins with the entire Justice League pitching in to rebuild the town.
Supergirl (Wednesday Comics): It is mentioned that the Super-Pets' rampage through Metropolis cost the city thousands of dollars worth of damage. How the city was restored is left unexplained.
In one issue, Superboy has a nice big fight scene with a robot, and then attempts to fly away. Lex Luthor of all people calls out from the crowd, asking why he thinks he can just leave Metropolis with the cleaning bill. Superman arrives and actually sides with Lex, saying that he always sticks around to clean up after battles.
Superman himself has actually been shown cleaning up after his particularly destructive battles. After Superman got his powers back post-Infinite Crisis and he and Lex Luthor had a huge smash-up in Metropolis, Supes was shown clearing debris and doing minor construction work (i.e. welding some support beams to the side of a slightly-damaged building to prevent it collapsing) potentially saving the city millions of dollars and months or years of work fixing the damage. In the Golden and Silver Age stories, more often than not, he would repair even minor damage with super speed after he caused it.
Krypton No More: After defeating an Alien Invasion, Superman, Supergirl and Krypto helped clean up the devastation caused by the battle.
In The Fall of Metropolis, most of Metropolis is reduced to rubble after Lex Luthor's missiles are set off. In the aftermath, Superman promises Lois he will help rebuild the city, brick by brick. He has already begun on his promise by starting with the Daily Planet globe which he and Perry White view as a symbol of hope for the city.
A Silver Age story has Superman being charged with, and convicted of, incredibly minor crimes that add up over the issue until they almost keep him in jail long enough for his accuser to perpetrate his evil plan.
In Marvel Versus DC, Superman and the Hulk are teleported to the Grand Canyon. Superman is relieved since it means no one will get hurt, and no collateral damage will occur. The Hulk doesn't care, with a "Let's just get ON with it" punch.
The Death of Superman: Without Kal-El to help clean up the aftermath, everyone in Metropolis is left trying to figure out what to do with the mess that was left. Flash and Green Lantern did help to repair the house of one family that was leveled in an early part of the battle.
The Flash: In a storyline Wally gets legally barred from Keystone City because of all the collateral damage that results from his everyday crime fighting. In order to make their case the city authorities even have accountants following him around and calculating the damage done in front of him. Also explained in another issue... where's it's pointed out that Wally is GREAT at construction... as he can build a bridge in minutes. Though, he does note that it's 'quick and dirty'... but, well... he could fix it up later.
The Authority, which takes a rather cynical view of superhero conventions, actually has the Authority helping out before and after supervillain attacks. Also somewhat unique in that the Authority often acknowledges that what they're doing will cause property damage and probably cost civilian lives. The characters justify it with the excuse that the bad guys would have done much worse if nobody had stopped them, but the fact that they openly acknowledge the cost of what they do is unique in itself.
Subverted with Batman as, being rich, he actually can afford to pay for damage.
In the after-effects of the "Sinestro Corps War", the dozens of alien lanterns who ended up on Earth decide to stick around for a bit and clean up their messes. John Stewart, a long-standing human GL — and more importantly, an architect in his day job — cleans up the skyscraper damage in Coast City all by himself.
Discussed in the first New 52 issue of Green Lantern Corps, when Guy Gardner can't get a job as a high school football coach, largely because simply having him on school grounds on a regular basis would send the school's liability insurance rates through the roof. In the same issue, it's played with a bit again in John's scene, where he tries to convince the company that hired him to design a new building to incorporate expensive measures to minimize damage if it happens to get caught in a supervillain attack or real knock-down-drag-out hero/villain fight. They disagree about whether the added expense is worth it.
Periodically lampshaded. Characters will sometimes make passing references to the city's "great public works" program, usually in the wake of yet another superhero battle. The introduction to the "Local Heroes" TPB includes a newspaper clipping that mentions Honor Guard using alien Applied Phlebotinum to repair damage after one of their fights.
Likewise, the first issue of the Homage run, "Welcome to Astro City" shows that years of these events have actually caused much of the city's populace to bond together in an extremely intense way, to the point that few (if any) avoid pitching in for clean-up and rebuilding.
Supersonic came out of retirement to bring down a robot in a clumsy manner of pure force, causing lots of collateral damage; he's angry because he wouldn't have done that in his prime, but he was indeed the only one available, no one was killed, and Astro City is great at coping with damage, so he can live with it.
