Did people in the past concern themselves with the welfare of the handicapped, such as the blind and the deaf, or did they neglect them?
Was e.g. the "Amnericans with Disabilities Act" a new threshold in this regard?
Caring for the old and infirm goes far further back than the historical record. Remains have been found in multiple neanderthal sites of individuals with old injuries that would have made them unable to fend for themselves. The best known example was a neanderthal found at Shanidar Cave I who had evidence of multiple deformaties and old partially healed injuries, leading to partial blindness, an unusable right arm, and a limp. There's no way he could have survived long enough for those injuries to show signs of healing without help. Another skeleton at the same site showed signs of degeneration in one leg that would have had him walking with a severe limp.
There's also the Old Man at La-Chappelle-aux-Saints, who was missing enough important teeth that some feel he may have either required a soft diet, or "prechewing" of his food from someone else. This theory appears to be not currently in very good smell, but it still has its proponents.
Both finds were of the neanderthal variety of hominid, from more than 60,000 years ago.
Neanderthals also were the first hominid known to create representational art, and to exhibit some kind of burial cerimony. So it looks like those things may have developed roughly at the same time.
Although this question has an accepted answer, I must question its applicability to the question as stated: All the examples cited by T.E.D. in his excellent answer are cases of individuals who were apparently born as healthy, non-handicapped people, lived productive or perhaps heroic lives and then, due to injury, war and/or old age, fell victim to disabilities. We can argue that in such cases, in compensation for a life of service or utility to their families and communities, such people were cared for even when they were no longer "productive".
But the question also (and perhaps principally) deals with those who were congenitally handicapped: Born with, or acquiring disabilities at an early age, as the result of some disease or genetic irregularity. People who never had the chance to lead "normal, productive" lives. On this point, History might indicate something different than the accepted answer:
Wiki: History of deaf education ...in contrast, those who were deaf in Ancient Greece were considered a burden to society and put to death.
Even in the recent past, we can cite such institutions as Willowbrook State School as engaging in far less than exemplary treatment of handicapped individuals.
So unfortunately, IMO humankind's record regarding this subject is by no means as rosy as has been painted by T.E.D.'s answer.
Based on the edit of the question to include the ADA, this bill was a landmark event in that it codified such consideration for the handicapped as required behavior for a very large and powerful nation, although its passing was the result of many years of work by various groups to engender national awareness concerning this issue.
Perhaps the beginning of this movement can be traced to the work of Alexander Graham Bell, and the life and work of Hellen Keller, among many others, starting in the late 19th and early 20th centuries. The idea was by no means novel when the ADA was passed in 1990.