A report from UBS found that wealth is a double-edged sword for today's millionaires, bringing plush comforts and a better lifestyle but also carrying increased stresses, anxieties and sacrifices with family and relationships. Today's millionaires also feel they are one stock-market crash away from losing their fortunes and that there is no such thing as "enough" wealth to feel secure. "Millionaires enjoy a great deal of happiness and appreciation for what they've earned," said the UBS Investor Watch report called "When is enough ... enough?" But "many feel stuck on a treadmill, without a real sense of how much wealth would make them satisfied enough to get off." Read MoreThe hottest luxury property market

The report found that 52 percent of millionaires expressed the feeling of being "stuck on a treadmill, but I can't get off without giving up my family's lifestyle." It said that while satisfaction goes up as wealth increases, 58 percent of millionaires said their lifestyle expectations have also increased—so the more they have, the more they want.

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The survey asked how much wealth millionaires aspire to have. Those worth $1 million to $5 million said they needed $5 million to $10 million. Those worth $5 million to $10 million said they needed $10 million to $15 million, while those worth $10 million or more said they needed at least $25 million. In other words, millionaires aspire generally to have more than twice what they have—even as they grow richer. Read MoreCan kids inherit too much money?

The survey also found that after the financial crisis, millionaires say they don't have enough wealth to feel secure. Sixty-three percent agreed with the statement that "one major setback (lost job or market crash) would have a major impact on my lifestyle." Wealth is also a blessing and curse for families. While millionaires say they value family above all else, and their wealth is aimed at improving their lives, they also say they sacrificed too time from family to make their wealth. Millionaires' "biggest regrets relate to mistakes they made with spouses and family members," the report said. They also worry that their fortunes may be spoiling their kids. Two-thirds said their kids "don't understand the value of money," and more than half worry their kids lack motivation and act entitled. As one multimillionaire respondent said in the survey, his son "sometimes adopts a superior attitude to kids from families who may not be as well off."