Like the other posts stated, dogs provide unconditional love. For example, you could have had a terrible day at work and come home to a dog who is very happy to see you. This makes you feel good.
In addition, dogs are also very therapeutic. For example, dogs are taken to nursing homes because it has been proven that they reduce loneliness and insecurity in the elderly. Therapy dogs also visit schools, hospitals, and special needs centers.
The companionship and unconditional love dogs offer are also a big plus. When I come home at the end of a long day, my dog greets me with sheer, unadulterated joy.
Like that first answer suggests this question is subjective, but it seems to me that many people would underline the faithfulness aspect of dogs. They will protect their owners with their own lives. This is an amazing thing. If we translate this into personal relationships, this means that a person would die for someone else. Also, dogs have been trained to save lives. Finally, there is an amazing poem that E. E. Cummings called "Good Dog." In this poem he captures one aspect of why dogs are such amazing creatures. In short, the dog wants to please so much that he even dies trying to please his owner. Try to read it, it may make you cry.
This will be an answer that is based purely on experience and, thus, be prepared for many different responses to it. The belief that dogs are best friends comes from the idea that they are so receptive to being so strong on interpersonal intelligences. This is a way of stressing that dogs can work extremely well in situations where people are involved. They are easily trained in terms of performing actions based on command. The notion of "Sit!" or "Speak!" or "Roll over!" are directives that arise from working with dogs. The idea of having a dog as protectorate also helps to embolden the reputation of a dog as a buddy. "Guard" dogs go better than "guard" cats or "guard" rabbits. At the same time, dogs have been depicted in media as more akin to being closer to people and the best friends people can have. Lassie, Rin- Tin- Tin, and in a more modern sense, Marley from "Marley and Me," are depictions of dogs that are strongly linked to individual experience and companionship.
In general dogs are the most friendly among all the animals kept as pets. Plus they express their affection and joy without inhibition. This lack of inhibition makes them appear more friendly than people, who generally have more inhibitions than dogs. Also there are many instances of dogs sensing troubles faced by people and make efforts to help them. Similarly there are many instances of dogs reacting with various degree of sadness to death or absence of people they are attached to. It is because of all these reasons that dogs have earned the adjective of "man's best friend".