You can give each of your parents (or anyone else) up to $10k as a gift and it will not be taxed as income to them (that doesn't change whether it's taxable to you). If you're married your wife could also give them each 10k. So you could give them up to 40k per year without it being taxable income to them.
BTW, I'm not a tax advisor, but some years ago I worked in the insurace biz, and learned a lot about this stuff. Still, check it out with a real tax advisor to make sure things haven't changed.
If your family members are in a lower tax bracket than you are, you might want to give them appreciated assets. When you do so, you will need to inform them how much you paid for the asset. Your basis would carry over to them. When they sell the asset, it would be taxed to them.
You may give up to $11,000 (at fair market value at the time of the gift(s)) per person per year without having to file a gift tax return. The gift must be of a present interest in property to qualify for this exclusion. If you are married, you and your spouse may elect gift splitting. In such a case, you may give up to $22,000 per person per year even if the property is held in your name only. You may give more than $11,000 ($10,000 adjusted for inflation) (or $22,000 if gift splitting) per person per year, but you would have to file a gift tax return. Unless you gave a very large amount, you would not likely incur any gift tax liability. However, you would use up some of your unified credit.
In addition to the annual $11,000 exclusion, you may pay money to a provider of medical care for medical expenses incurred by anyone, and you may pay tuition for another person directly to the school. The amounts are not limited and they are all excluded from taxable gifts. The money must be paid directly to the school or the medical provider and not to the individual.
Bottom line, you pay, they don't.