You probably know how some people give charitable donations as gifts... and that can be a really great gift idea in itself. (Just send them a card telling them you've donated some money to a charity you both approve of; or some charities will send the card themselves.) There are other ways, though, of giving so as to benefit the receiver and others...
Remember Aunt Mary and the chocolate chips? - she makes all of those cookies for the neighbors. One lady I knew of, in her nineties, took the greatest of pleasure and pride in making banana bread for everyone she knew. Old dead bananas she was given plenty of (!) - but the butter, eggs, nuts, and whatnot might be a little pricey on her pension... Hmm, there’s a gift message there.
Do you have a still-dynamic loved one in a nursing home or an assisted living facility? - group activities are very important there. Consider giving a gift that enables this person to share with others - something like a puzzle or a game to be played with others; or a packet of cellophane-wrapped candy canes to pass out; or a whole bunch of little gaily wrapped toiletry gifts to pass out to everyone else there. Or you could give your time in leading a songfest or other fun activity for everyone.
Another idea for an elderly person who can no longer get out and about is to give her something like the promise to donate a lot of produce to a food bank on her behalf - perhaps along with a weekly update (and photos?) of what your garden looks like during the growing season.
Your brother-in-law would love to be able to be a scout leader, but your sister and the baby would be too disturbed by having the troop in their tiny apartment... Can you offer him the use of your living room (and perhaps refreshments) one night a week?
Is your young son very moved by the plight of homeless pets? Perhaps he’d love to have you donate money to the humane shelter in his behalf. Or you could give him a collection of items needed at the shelter for him to give as a gift to the critters.
A friend of yours volunteers as crafts director at a nursing home but is running out of imagination... Give her a packet of craft ideas, and maybe some harder-to-find supplies to go along with them - if not a promise of your assistance with some of them.
Got a friend who homeschools her kids? She’d probably love an afternoon off a month while you teach something!
What about parents of school-age children who aren't rich but hope their kids can go to college? Perhaps those adults would far more appreciate a donation to the kids' college fund rather than a tangible gift they don't really need.
(Great gifts can be anything!)