I'm turning 62 this year and I'm considering claiming my retirement benefits early, since I was just denied disability benefits. If I do, will this lower my wife's benefits too?
As you know, claiming Social Security before your full retirement age, which is currently 66, will lower your benefits permanently. Social Security reduces your benefits using the early retirement penalty so that you'll receive the same amount between now and the average life expectancy, whether you claim at age 66 and get the standard amount, age 62 and get a smaller amount, or 70 and get an increased amount. That said, if you claim benefits early but you live past a certain age—called your "break-even point"—you will wind up collecting less in total lifetime benefits than if you had waited to claim them at full retirement age.
Now, to answer your question: If you claim your Social Security retirement benefits early, this will not affect your wife's dependents benefits, which are also called spousal retirement benefits. As long as your wife waits until her full retirement age to claim her spousal benefits, she can collect the full amount. Because dependents benefits are based on your primary insurance amount (which is based on your earnings record at your full retirement age), whether or not you claim benefits early doesn't affect the amount of dependents benefits your spouse can collect.
Spousal retirement benefits are half of your primary insurance amount – that is, half of what you would have received if you had waited until full retirement age to claim benefits. However, if your wife claims the spousal retirement benefit before her full retirement age, her spousal benefits will be lowered permanently.
Survivors benefits are handled differently. If you claim retirement benefits early, this will lower your wife's survivors benefits (also called the "widow's benefit" or "deceased husband's benefit), should you die before her. This is because at your death, your wife will be able to collect the same amount you were entitled to before you died. If your retirement benefit was lowered because of early retirement deductions, or increased because of delayed retirement (up until age 70), your wife's survivors benefit will be similarly increased or decreased.
Also, if your wife were to collect the survivors benefit before she reached full retirement age (anytime from 60 to 65), her survivors' benefit would be decreased. So if you collected retirement benefits early and then your wife collected her survivors benefits early, she would only get a small portion of your full retirement age benefit. (There is an exception here if your wife is caring for your dependent minor or disabled children: In this situation, she would not get an early retirement penalty regardless of the age she claimed this "mother's benefit.")
There are different strategies that couples can use to maximize their benefits, including "claiming and suspending" and collecting dependents benefits from each of your earnings records. To find out more, see Nolo's article on how couples can maximize their Social Security benefits.