Buddhism is an atheist religion that does not rely on or need gods. Gods are not the cause of the samsaric system that is responsible for the cosmos. Nonetheless, Buddhist texts often talk of gods (just as the Old Testament does), although they are not the same kind of eternal being that Westerners expect. For this reason, many call Buddhism an atheist religion. There are no easy words to describe the nature of the supreme beings that inhabit Buddhist stories without using saying "gods", however, it is certainly untrue to say that Buddhism is formally theistic, therefore, it is best described as atheistic.
"Buddhism" by Christmas Humphreys (1954): Humphreys was President of the Buddhist Society, London, from its foundation in 1924 until its Silver Jubilee in 1954. On page 79 under title "No God, No Soul" he writes "As between the theist and atheist positions, Buddhism is atheist".
In a prominent book by one of the founders of academic religious studies, "The Varieties of Religious Experience" by William James (1902) [Book Review], James says "there are systems of thought which the world usually calls religious, and yet which do not positively assume a God. Buddhism is in this case. Popularly, of course, the Buddha himself stands in place of a God; but in strictness the Buddhistic system is atheistic"1.
Tanebaum, Center for Interreligious Understanding, publish statistics on world religions and note that Buddhists can sometimes be double-counted because they are included as "religious" and "atheist"3. This only happens, of course, when we fail to realize that "non-religious" means non-religious, and "atheist" does not mean non-religious. So if you add "atheists" to "religious" stats, you will end up double-counting Buddhists.
And for fairness' sake, here are some who err on the side of calling Buddhism theistic:
"The Phenomenon Of Religion: A Thematic Approach" by Moojan Momen (1999) [Book Review]: The worship of deities has continued in many forms of Buddhism despite Western scholars thinking that, because of their texts, Buddhism was atheistic5. Note that Momen is a Bahá'í who therefore believes in a certain unity of all religions under a single god, therefore he comes from a slightly biased position.
Religion is complicated, and there is often a discrepancy between what the cultural followers of a religion do, and what the religion formally asserts. "Cultural Religion Versus Scholarly Religion" by Vexen Crabtree (2013) explains how it is normal for a religion to be officially one thing, but for the grassroots masses to have a variety of cultural beliefs and practices, sometimes making it hard to clearly define what a religion is.
The Gospel According to Woman: Christianity's Creation of the Sex War in the West (1986). Subtitled "Christianity's Creation of the Sex War in the West". Hardback. Published by Elm Tree Books/Hamish Hamilton Ltd, London, UK.
Buddhist Scriptures (1959). Published by Penguin Books.
Draper, John William. (1811-1882)
History of the Conflict Between Religion and Science (1881). 8th edition published by D. Appleston and Co, New York. Digital version accessed via Amazon.co.uk.
Buddhism (1954). Christmas was President of the Buddhist Society, London, from its foundation in 1924 until its Silver Jubilee.
The Varieties of Religious Experience (1902). From the Gifford Lectures delivered at Edinburgh 1901-1902, first Edition printed 1960. Quotes from fifth edition, 1971, Collins. [Book Review]