Can I still make a $10,000 gift to an individual without having to worry about gift taxes?

Yes. On January 1, 2018, the amount of what’s called the annual exclusion amount from gift taxes was increased to $15,000. There is no problem with you giving up to $15,000 to any one individual in any one calendar year without the necessity of filing any gift tax returns. $10,000 was the gift exemption amount for many years and it’s the sum what still tends to stick in people’s minds even though it’s been increased over the years.