Check out exchange websites
The second option—the major new choice—is to shop for a plan on the federally run website, HealthCare.gov, or on a state-run health exchange. HealthCare.gov offers plans for 36 states, while 14 states and the District of Columbia are operating their own exchanges.
Although HealthCare.gov's tech troubles have made it difficult for many people to enroll in plans so far, federal officials predict that it will be operating smoothly enough by the end of November that millions of people will be able to use it and buy coverage.
Though there's no obligation to sign up on the government-run exchanges, Collins said it is "very important" for consumers to consider using the them, as plans sold on them are the only ones eligible for federal tax credits, or subsidies, to offset premiums and out-of-pocket costs.
"You might want to look at whether you're eligible for a subsidy," Collins said. "It might reduce your costs, and you might get a better policy."
Subsidies are available to individuals whose adjusted annual gross income is less than about $46,000. The income maximums for subsidy eligibility increase with family size, up to a family of four, whose maximum income to get subsidies is $94,200.
For Bridget Wood Moreau, a 46-year-old homemaker from Estes Park, Colo., buying on her state's exchange offered a significant cost-savings for her family. She had received a cancellation notice for her own Rocky Mountain HMO policy, and Humana said her husband and four kids would have to re-enroll in a policy that will expire next year or choose new plans.
(Read more: Obamacare explained)
Beforehand, both policies had a combined $1,415 in premiums and deductibles of $12,500 a year, she said. Because of Moreau's ulcerative colitis, a recent scoliosis surgery for her daughter and other costs, the family's annual medical bills had routinely topped $30,000 and were "unsustainable," she said.
But this week, Moreau enrolled in a Kaiser Permanente plan on Colorado's exchange that had a monthly premium of "$1,133 for all six of us, and zero deductible," she said. With a monthly subsidy of $303 they qualified for, the family will pay $830 a month.
"I'm ecstatic," Moreau said.
Check out whether your insurer can recommend another plan
Cancellation letters being sent out by insurers will usually contain information about certain other plans offered by the same insurer, Collins said.
Independence Blue Cross in Philadelphia recently sent out the second of what will be a series of three cancellation and informational letters to 25,000 individual policyholders, which make up about 40 percent of IBC's individual policy business.
The letters contain side-by-side comparison of current plans with three other policy options from the insurer, according to Brian Lobley, IBC senior vice president for marketing.
Obamacare subsidies and regulations on how insurers deal with customers with pre-existing conditions mean that "a good majority of the folks are actually going to have a more affordable policy," he said.
Independence also plans to make "outreach calls" to those who don't respond by choosing a new plan, Lobley said. "They're IBC members, so we want them to stay IBC members."
(Read more: Obamacare deadlines you need to know)
To that end, IBC—like other insurers—is not pointing out that customers can check out competitors' offerings.
But Collins said it's worthwhile for people to shop around for coverage because "there's a lot of variability between plans," even when they cover the same percentage level of benefits.
Plans can have significantly different premiums, as well as varying deductible and other out-of-pocket costs, and network providers—all things that customers need to weigh, she said.
Look for other options
"You can also consult a broker or 'navigator' to help you with the process," Collins said .
Brokers are the traditional insurance brokers, while "navigators" are a new class of helpers created by the ACA who assist people with shopping and buying coverage from the government-run exchanges.
Collins also noted that people can check out online brokers such as ehealthinsurance.com, getinsured.com, gohealthinsurance.com, which offer thousands of plans nationally.
A number of those Web brokers are expected to be connected soon to the federal exchange HealthCare.gov, so that they can sell plans that are eligible for subsidies.
—By CNBC's Dan Mangan. Follow him on Twitter