In short, yes. Hinduism defines a concept of karma which is loosely the same as karma as it is known in the English speaking world.

A person's (or being) actions have a direct and indirect effect on their karma. Think of it like a credit score, only more complex. At a high level, there are 3 dimensions or energy levels that count towards your karma - sattwa, rajas and tamas. Based on each action, inaction or behavior you score on these 3 scales. Sattwa is said to be what one should aim for as it includes all the good qualities and powers - good as in good in a general betterment-of-human-life sense. The gunas are not be confused with positive, negative and neutral as sattva which you might think is neutral doesn't count if you remain neutral in some scenarios. (Aka Dante's quote). 

(See Bhagavad Gita chapters 14, 17, 18 on understanding the different modes.)

As long as you score on rajas and tamas, no matter how you do on sattwa, you are doomed to be reborn.

Edit: As cheenbabes pointed out in the comments, as long as you score on ANY gunas you cannot have Moksha. However, sattwa is the most ideal level for life on Earth.

One's life's purpose is to attain Moksha and escape the world of birth and death. The concept of Moksha itself is deep and involves the Brahman which is a different topic altogether.

Spiritual evolution in the Vedas states that beings begin at lower life forms such as insects and work their way up through reincarnation through the bodies of plants, birds, animals, and finally humans. The belief that "once a human, always a human" is not supported by Vedic philosophy. One reason for this is verse 8.6 of the Bhagavad Gita:

> Whatever state of being one remembers when he quits his body, O son of Kuntī, that state he will attain without fail.

This implies that if one receives the next body in order to suit the consciousness at the moment of death. In other words, if your desires can be more easily fulfilled in the body of a dog, you may receive that next body.

One example is the story of Jada Bharata in [Srimad Bhagavatam][1] . In summary, King Bharata, although very highly advanced in spiritual practice, became attached to a deer, and because of thinking intensely of the deer when he died, he took his next birth in a deer body. 


  [1]: http://www.vedabase.com/en/sb/5/7