my ducks and geese are self-sufficient, good foragers, and I enjoy watching them. They are far less trouble than chickens once they are grown and have eggs just as good. Don't require much feed in the summer (geese never).
I have ducks because they're less hassle for me than chickens. That may not be true for everyone, but it is for me. With ducks I don't have to worry about them flying over the fence, getting frostbitten, or pecking each other's feathers off.
Plus, they lay better than my chickens. If my Khakis keep it up, they'll be laying twice as many eggs as my chickens per year. Also, their eggs are larger, better for baking, and have more flavor than chicken eggs.
They're also ridiculously cute and have great, wacky personalities.
I have ducks and geese because sometimes I get burned out on eating chickens
Well, that and a bunch of other reasons.
Duck and goose eggs are fantastic to bake with. Once you've baked with them you won't go back to chicken eggs ever again. They make everything light and fluffy.
They're excellent at keeping bugs down. Where chickens will eye a slug, ducks will gobble them up. Geese also have a fixation with dandelions - the easiest way to deal with a dandelion infestation is to get a gaggle of geese. In addition, geese can be trained to weed your garden for you. That gives you a flock of gardeners working 24.7 to naturally fertilize and weed your garden, rain or shine. And for free.
I live harvest down when the geese are molting (and I'll probably live harvest from ducks, as well, if I can ever get around to it). I make pillows, quilts, and dolls. I save some to put in rabbit nestboxes in case the does don't pull enough fur and then sell the extra.
They are tasty. Goose and duck taste more like beef than like chicken. It's nice to have a little variety on the plate.
They're just _fun_. If you've never had a gosling before then you're missing out. Where chicks and ducklings are more skittish and tend to run away, goslings are always happy to come up and chat with you. They don't seem to care what you say, they just want to sit and talk for a while.