We go to a church that has a large number of disabled and disadvantaged members, so most of our giving is directly to people we know for specific needs.
I used to be of the mindset that poor people often handle their money badly, and we shouldn't exacerbate it by helping them out. Then I actually got to know some poor people, and realized that in their situations I wouldn't do any better. Everyone makes minor money mistakes here and there, but the lack of true safety nets often makes for disproportionately huge impacts. We help provide a safety net for people who have none (and if you think the government provides a great safety net, just wait until you have to take a sick kid to the doc and your car breaks down. Four expenses in one-alternative transportation to the doctor, doctor bill, car repair, and lost wages, only one of which the government will potentially help with).
I am also absolutely disgusted by the state of mental health care in this country. Even for people on medicaid, something as simple as weekly counseling is $160/mo out-of-pocket, which for many is 10% of their income. The free counselors through DHFS are really hit-or-miss, and there is currently a one-year waiting list to start seeing one. We help out a lot on mental health copays.
We also do some longer-range help, like giving away LEDs to people who are struggling with electric bills, doing preventative maintenance on vehicles, etc.