hmm ... I assume no. what about a cuckoo? Cuckoo doesn't have own nest, they lay eggs in another's bird nest and leave it there to be raised by that bird.
But I think mostly yes. For example falcons do not build their nests, but they use old nests of other birds or they are nesting only on rocks where is a nest-like space, but they don't build it. Kestrels (falco tinnunculus ) are nesting in flowerpots on balcony or garden in cities because there are so many of them ... Most of falcons use old crow's or raven's nests though.
But basically I think all birds (most of the birds) do have nests because it's only natural for them to try to keep their chicks being safe.
I guess u could say all birds have some sorta nest. It depends on where the bird comes from, take australian birds like parakeets and cockatiels, they nest in nestboxes, in the wild they nest in hollow tree holes.
Some birds make nests from mud. So yes all birds have some sorta nest.Do all birds make nests from grass and stuff like that? No.