Medicare Part A is free for many people, because you've essentially prepaid the premiums through decades of taxes. Part B will cost $121.80 per month for new enrollees in 2016 (more for high-income earners), and the average Part D plan is expected to cost $41.46. (See Medicare 101: Do You Need All 4 Parts?)

On the surface Medicare looks relatively reasonable compared to private insurance, so why wouldn't you enroll as soon as you become eligible? Let's take a look at several situations in which your finances and your health might be better served by delaying enrollment.

If you're still employed when you turn 65, you can keep relying on your employer's group health plan; however, seemingly arbitrary rules determine whether you must also enroll in Medicare. If you work for a company with 20 or more employees, then you don't have to because Medicare will treat this coverage as your primary insurance. If you work for a company with fewer than 20 employees, then you'll probably need to enroll in Medicare because the company's insurance plan will usually expect Medicare to be your primary insurance. There are exceptions to the fewer-than-20-employee rule, though, so if you're in this situation, ask your employer how Medicare treats your insurance. (For more, see The Employee's Guide to Medicare.)

Assuming you have the option to keep relying on health insurance from your employer, it can be less expensive than enrolling in Medicare. The premiums might be cheaper, as your employer covers much of their cost. Even if the premiums are higher, the coverage might be better, saving you money when it comes time to visit the doctor or get a lab test. Just like private health insurance, Medicare has deductibles you have to meet and coinsurance you have to pay. Furthermore, if you don't qualify for premium-free Part A because you don't have enough work credits, it could cost you as much as $411 per month in 2016. Purchasing an optional Medigap​ policy will add another couple of hundred dollars a month to your bills. (For more, see When to Get a Medigap Insurance Plan.)

It can also be simpler to stick with a plan you already know instead of learning how to swim in the alphabet soup that is Medicare. In addition, you may have dental and vision benefits through your employer that you wouldn't get from Medicare. (For more, see Medicare Mythbusters: What You Don't Know.) That being said, your employer's plan might be inferior to Medicare, in which case you'll probably be all too happy to switch – unless you have a health savings account (HSA).

Are you using an HSA as a retirement tool? If so, you probably want to be able to keep making contributions for as long as possible to get the most benefit out of this uniquely triple-tax-advantaged account. This is especially true because once you're 55, you and your spouse can make catch-up contributions of $1,000 each to your individual HSAs. The problem is that once you enroll in Medicare, you can no longer contribute to an HSA. (For more, see How to Use Your HSA for Retirement.)

If you start claiming Social Security benefits before you turn 65, the government automatically enrolls you in Medicare Parts A and B when you reach 65. You can opt out of Part B if you're receiving Social Security payments – but not Part A. So contributing to an HSA means that you must be able to afford to postpone Social Security. It also means manually disengaging from Part B if you've been automatically enrolled.

According to the Kaiser Family Foundation/Commonwealth Fund 2015 National Survey of Primary Care Providers, while 93% of non-pediatric primary-care physicians say they accept Medicare, only 72% say they are accepting new Medicare patients. If your primary-care doctor won't accept you as a Medicare patient, you might be disinclined to enroll. Still, chances are you see a variety of doctors for a variety of reasons, so you need to find out what each practice's policy on Medicare acceptance is and figure out what type of insurance coverage will be most cost effective for you overall. If you're thinking about switching providers, be aware that some don't accept private insurance either. (For more, read What To Do When Your Doctor Doesn't Take Medicare.)

Enrolling in Medicare is optional, but not everyone wants it. If you never enroll or you enroll late, you're missing out, in a sense: You've been paying Medicare taxes throughout your working years in the form of the 1.45% of your paycheck that both you and your employer have contributed, effectively reducing your pay by about 3% for every year you paid FICA taxes. But when the quality or cost of coverage – or maxing out HSA contributions – are concerns, it might make sense to put off enrolling as long as possible.