But the good news comes with a challenge for health officials: how to keep persuading people to get vaccinated when swine flu infections are waning.
"We're worried that people might be thinking out of sight, out of mind," said Tom Skinner, a spokesman for the Centers for Disease Control and Prevention.
Health authorities say that getting vaccinated could be a lifesaver if a new wave of illnesses materializes this winter.
The swine flu vaccine supply started with just a trickle from manufacturers in early October, leading doctors to reserve it for pregnant women, people with asthma, children and young adults, and others at high risk of becomingly severely ill.
But now 95 million doses are available, and 10 million more are coming out every week. Health officials in 24 states have lifted their recommended restrictions, as have communities in other states, said Paula Steib, spokeswoman for the Association of State and Territorial Health Officials.
The vaccine is so abundant in some places that it is now being given out at drugstores, in addition to doctors' offices and clinics.
Some places are seeing pent-up demand. In Minnesota, a county health department clinic in suburban Minneapolis opened up early and gave out 150 shots in the first two hours on Wednesday - the first day vaccinations were available to everyone in that state.
Among those in line was Bill Haugen. He escaped swine flu when it swept through the collection agency where he works, and he was worried about its return. "I don't want to bring it home to my kids," said Haugen, 31, who has two young children.
More than 100 mostly healthy people showed up for vaccinations at a Walgreens pharmacy in downtown Chicago on Tuesday, the day the Illinois' public health department lifted its restrictions.
Larry Richmond, a Chicago lawyer who is not in any high-risk group, stopped at the pharmacy Wednesday morning on his way to work. "I'm concerned about the spread of the virus and thought it the prudent thing to do," he said.
In Atlanta, an Emory University student health center started offering the shots to all comers last week, just before students went on winter break. Hundreds showed up.
Demand is also high in parts of the country that still have widespread reports of swine flu illness, including New York and parts of New England, health officials say.
But demand appears to be down in many areas where infections are dropping - and more and more states are falling into that category.
In late October, 48 states were reporting widespread swine flu illnesses. That turned out to be the peak of the fall wave. By the first week of December, only 14 states had widespread cases, and experts believe the count has fallen more since then.
CDC officials estimate the virus has sickened one in six Americans - 50 million people - and killed about 10,000 since the virus was first identified in April. It has caused unusually high numbers of serious illnesses in young adults and middle-age people.
But overall, it is not causing more deaths and hospitalizations than ordinary seasonal flu, and many people are not particularly worried about getting it.
Last week, the Department of Health and Human Services launched a new campaign to keep up interest in vaccinations, warning that flu is unpredictable and that another wave of cases could hit this winter.