There are a number of similarities between the two religions; probably because Buddha himself was Hindu before his enlightenment. Both believe in reincarnation, life in physical form after death. Although this seems desirable, it means one must deal with the many hardships and sorrows of human existence all over again. One hopes to break this cycle and enter into a heavenly state. Both are religions of salvation; both believe that by breaking the cycle of reincarnation one enters into a state of eternal rest. From there, there are significant differences.
Hinduism believes that one is born into a caste, or social status based on ones previous life. Although the Indian government has outlawed the system, belief in it is widespread. Buddhists do not practice the caste system, rather they do believe that ones past life has some determination on ones future life; but it does not bind one into an ironclad social sect. They do believe that reincarnation continues until the cycle is broken. They also believe that all suffering is caused by desire; and one can only break the cycle of suffering by ending desire.
Hinduism does contain a large pantheon of gods; but it is not necessarily true to state that Buddhism has no Gods. There are variations of Buddhism, one of which, Mahayana, or the "greater vehicle, worship Buddha himself as a god. This sect is popular in Korea, Japan, and China.
Hindus believe that if they lead a balanced life of obedience to the moral and spiritual law, pursue honest prosperity and enjoy social and physical pleasure in moderation, they will achieve salvation and enter moksha, a state of heavenly bliss. Buddhists believe that when the cycle of reincarnation is finally broken, they enter a similar state known as nirvana.
One final but important difference. Buddhism is a missionary religion which actively seeks converts. This accounts for its spread throughout east Asia. Hinduism is not missionary, but is rather culturally defined. It is seldom found other than among persons of Indian ethnicity.