Yes, aid relief donations make it to their intended destination if you are contributing to an honest, reputable group. Always research the agency before donating. There are many scams playing on the generosity of people. The National Better Business has a website that gives information, evaluates and reviews charities. The American Red Cross is one of many that meets all 20 of the BBB's standards for charity accountability.
It very much depends on the charity if relief funds and donations actually make it to the people that they are intended to help. Different charities have different overhead and costs involved with their work. There are also those charities who are shadier and more concerned with corruption and their own profits. For the most part though, I think that people get helped a great deal by charitable donations.
Most organizations who promise to send your relief donations to specific areas deliver on their promise and are made up of selfless people trying to make the world better. There are some scams and swindlers out there, of course, but those are usually shut down pretty quickly and swept away.
It has been shown that sometimes aid intended for developing countries does not always reach its intended destination. There is a lot of corruption in countries that need aid, and resources often end up in the hands of rich officials. Furthermore, aid agencies in the West often take part of the donations for their operating costs.
There are so many reasons why direct monetary aid and donation of goods are not great for many developing countries, and one of them is the allocation of money within the source country. Corrupt governments and militias can often fairly easily embezzle funds from the aid, and ultimately are counter productive.