I kind of agree with AdA, kind of. I am angry that governments have largely got out of the social housing business, though some projects are being built again. Deinstitutionalization in theory is a great idea - integrate people into society, but there is no social net to help, so many end up on the streets.
Gentrification has removed a lot of the lowest-priced permanent addresses, mainly the SROs (rooming houses), and the issue of the "hidden homeless" and the near-homeless is big. The pandhandlers are the tip of the iceberg.
That said, I would rather pay more in taxes to make a bigger dent in this (along with higher taxes for better public transit, tuition fee freezes and/or reductions, other social programs, etc), and would be pleased to do so if it got more homeless off the streets. That would do even more good than to give to the UW or change to the homeless, and in many ways, it is better to give a decent amount to UW or other charities (Salvation Army, ShareLife, etc), for service that will help than to give change, but I refuse to take the "it will only go to booze" attitude (why should I care, in a way), so once in a while I still give a little bit.
That said, there's a "hard core" that will continue to remain homeless - charities like the United Way and more shelters will help. I could not afford to give change to all pandhandlers I come across anyway (I work in an area with a high concentration of homeless).
But a lot of people do not share my centre-left views, so that all but rules out my ideal answer.