Only 6% of over-65s describe themselves as "old" and only one in three has given serious thought to the care they might need in future, suggests a poll.
More than 2,000 people aged 65-93 were surveyed by YouGov for a firm providing support services for older people.
Almost half of those questioned (47%) complained of ageism.
Concern about being seen as a burden means older people can sometimes fail to make adequate plans, says Invicta Telecare, which commissioned the poll.
The online survey, carried out last month, found that almost two-thirds (62%) were concerned about being seen as a problem by society.
And one in five of those polled (21%) worried about being thought of as a burden to friends and family as they grew older.
The survey also looked at older people's attitudes to their age. About 63% agreed that being old was just a mindset and refused to define themselves as old.
More than a third (39%) said they were happier than at any time, and 42% described themselves as "more tolerant".
But 48% said they thought their generation was "ignored". More than a third (37%) felt treated disrespectfully because of their age.
About 34% complained the word "old" was derogatory, while 27% disliked the word "elderly" and 30% objected to being described as an "OAP".
The Queen at 87 and Dame Judi Dench at 78 were hailed as positive role models for their generation.
Some 83% agreed that "older people can still make a huge difference to this country".
'Freedom and independence'
Official figures indicate that the number of over-65s in the UK is likely to nearly double to around 19m, or a quarter of the population, by 2050 - up from 10m in 2010.
There were three million people aged over 80 in 2010. This figure is expected to reach eight million by 2050.
Wendy Darling of Invicta Telecare said: "It's important to tackle the old-fashioned taboos that many are coming up against.
"We all need to be prepared to discuss this subject more openly within our families and make sure people get access to the right information and help for them.
"It's clear many worry they will lose their identity and be seen as a problem as they grow older so it's important not to underestimate the support out there which will give full control of your freedom and independence."
A spokeswoman for the Department of Health said: "Older people play an incredibly important role in society, and are the lynchpins of many families and communities. They should be able to look forward to a happy and healthy old age, without having to face discrimination or catastrophic care costs.
"We are reforming the care system so that people will finally be able to plan for the care they might need in their later years and we've banned age discrimination in health and social care, so there is no room for any assumptions about a person's age."