“[…] it is now generally accepted, but not conclusively proven, that petroleum formation predominantly arises from the decay of organic matter in the earth. […] alternative theories should not be dismissed until it can be conclusively established that petroleum formation is due to one particular aspect of geochemistry.”
Source: James G. Speight (2006), The Chemistry and Technology of Petroleum, Fourth Edition
The alternative theories, classed together as 'Abiogenic' explanations have existed in various forms since the 16th century. These theories seek to address unexplained problems with the mainstream 'Biogenic' viewpoints.
For example, the 'lighter' hydrocarbon deposits (gas and light oils) tend to be found at greater geological depths (and heavier ones, like coal, nearer the surface). The exact opposite of what the 'Biogenic' theory would suggest.
One of the main arguments supporting the standard 'Biogenic' theory is that the deposits universally contain ratios of helium isotopes consistent with living matter - but recent (2006) discoveries in South African gold mines have shown significant colonies of bacteria living in basalt rocks at depths of several kilometres. (Source: New Scientist.) - opening the question of whether similar organisms could have provided the observed helium isotope balance in hydrocarbon deposits that actually originated abiotically.
(Also see (2017): Subduction zone forearc serpentinites as incubators for deep microbial life)
Further reading. The main Abiogenic petroleum pages at Wikipedia.