Actually, one person can make a great impact in someones' life. If you are cold-hearted and don't even try to accomplish anything, then you'll never know what kind of impact can happen. Mother Theresa was one woman, but she did a lot of good. A friend of mine, Wanda Gibson was one woman that established a pantry that fed tens of thousands of familie in my county.
Unfortunately, it is poor motivation like that stated in the OP that make this world such a bad place to live. If you and everyone else that do not care, started to care about others that you don't know, we wouldn't be in the mess that we are in. Why do we need government welfare for health, economy, employment and everything else? Because many have failed to provide your community the same things. People have at many times and many places banded together to offer such services which have saved many lives. That hospital you go to for care? Most were established by Christians centuries ago. That kid a childless couple wants to adopt? (Modern) Adoption was created in the 1800's by a minister. Most modern welfare initiatives have their roots in one or a few people accomplishing incredible goals because they wanted to get something done.
I'll give you a real-life example of what one person can do - certainly a trivial situation, but I think the result was well worth the cost:
I was leaving GDC in San Fransisco, when I saw a man begging about 2 blocks from the conference center. I felt like I needed to help me. I recognize the fact that most people begging/homeless are simply wanting money for booze or drugs, so I was intent on only giving him a dollar or two, but offering to take him out to eat. If he accepted the offer of eating, I would consider giving him more money.
So I gave him a few dollars - $4. I then asked him if he wanted something to eat. He replied that he hadn't eaten all day, and he was really hungry. I told him that I'd take him anywhere he wanted to eat. Mind you, this is downtown San Fran and there were very expensive restaurants right in front of him. Rather than request a $50 meal, he asks if I can walk with him to a taco joint two blocks away. I was unfamiliar with the place, but seeing as we were on a major street, I thought there was no harm in walking with him.
As I walked with him, he started talking about why he was in SF begging in the first place. It turns out, he was lured to SF by a friend for work at an auto detailing shop. He took a bus to SF from Oakland, and moved in with the friend to start work on auto detailing. After a week of work, he asked his friend for his earnings so he could send money back to his family, and be able to eat, ect. Instead, his friend kicked him out of his house onto the street. He had slept on the street for a day until he found a shelter. Unfortunately, the shelter had no food, and no way of helping him get back to his family in Oakland. He had been begging for a few days to get the money for bus fare back to Oakland, but due to the expense of eating in SF, he wasn't able to get a lot of money together to return home, but was able to call his family and try to arrange transportation in about a week.
At any rate, we finally found the place to eat which was arguably the cheapest place in SF (still about $5/meal), and I ate with him. Instead of ordering something expensive, he bought two of something, and made sure he saved the other taco so he would have something to eat tomorrow for a meal. After finding everything out about his story, I made sure that before I left him, he had a ticket in his hand to ride the bus back to his family in Oakland.
Now, such a story isn't some monumental tale of saving a poor person from the fires of war, or certain death, but I managed to help a guy get home, and make sure he didn't have to sleep at a shelter or beg for food. The total cost to me was about 1 hour of time and $25 between bus fare, food and what I gave him initially. Maybe it changed his life, maybe it didn't. All I know was that it was worth it to get a priceless, crazy look from a black business guy in line at the taco restaurant - seeing a random white kid sitting and eating with a homeless black guy shocked him.