Are There Any Other Birds That Lay Their Eggs In Other Birds' Nests Like Cuckoos Do?

Yes, the parasitic weavers and whydahs of Africa do. These birds live throughout large parts of Africa south of the Sahara desert and on savannah and open plains and in villages, gardens and open woodlands. Like cuckoos, they do not build their own nests, but lay their eggs in the nest of other birds, especially those of small waxbills.

Unlike cuckoos, however, the whydahs are not so cruel. They do not throw out the eggs and small baby birds of the host species of bird in order to take all of the food brought into the nest by the adoptive parents. Instead, the baby bills convince the waxbill parents that they are just extra chicks that belong to them; they mimic the waxbills' chicks by having the same bright skin colour inside their mouths and the exact number and pattern of black spots on their palates.

When the young whydahs and waxbills open their mouths for food, they all look the same, so the parent bird feeds all the growing chicks.

The most common North American bird that is a "nest parasite" -- lays eggs in other birds' nest -- is the brown-headed cowbird, a robin-sized songbird.
Cowbirds developed this adaptation in order to keep up with migrating herds of buffalo (cows) over the Great Plains. Creating a nest and raising a brood take a lot of time and energy, so the cowbird enlisted the unwitting aid of other bird parents to to this for them.
The cowbird lays its eggs in the host bird's nest and throws out existing eggs. The cobirds hatch first and are bigger that the host's chicks. But the host cannot disinguish between the cowbird chick and its own, so feeds  the invader. The juvenile cowbird also kills the host's chicks sometimes.
In some areas, cowbird-eradication efforts are under way because of nest parasitism's effect on declining species of other birds.

In the U.S. Cowbirds also lay their eggs in the nests of other birds, like the Black-capped Vireo.  Cowbird chicks grow larger than the vireos, so they can reach higher, get better feeding attention from the vireo parents, and even push the vireo step-siblings out of the nest.

Yes, according to the National Audubon Society, the Brown headed Cowbird does. Cowbirds are brood parasites,laying their eggs in the nest of other birds and leaving them to the care of foster parents. Unlike parasitic Old World cuckoos, which lay eggs closely resembling those of host species, cowbirds lay eggs in nests of more than 200 other species, most smaller than themselves. Some hosts eject the unwanted egg, others lay a new nest linning over it but most rear the young cowbird as one of their own. The young cowbird grows quickly at the expense of the young of the host, pushing them out of the nest or taking most of he food.