Sure, check your dictionary.
Capitalized nouns refer to a specific being/object (or in this case, concept of a being). 'God' is a name, as Odin or Thor or Vishnu would be a name.
Titular, aspecific, forms are lower-case. "President of the United States" vs. "president of a company."
The OED:
God
" noun 1 (in Christianity and other monotheistic religions) the creator and supreme ruler of the universe. 2 (god) a superhuman being or spirit worshipped as having power over nature and human fortunes. 3 (god) a greatly admired or influential person. 4 (the gods) informal the gallery in a theatre.
In definition 1, the Abrahamic deity is capitalized, being a proper noun. In other definitions, particularly the second (the titular form, as noted earlier), capitalization is incorrect.
also, wikipedia does it short and sweet:
The names of gods are capitalized, including Allah, Vishnu, and God. The word god is generally not capitalized if it is used to refer to the generic idea of a deity, nor is it capitalized when it refers to multiple gods, e.g., Roman gods. There may be some confusion because the Judeo-Christian god is rarely referred to by a specific name, but simply as God (see G-d#Laws of writing divine names). Other names for the Judeo-Christian god, such as Elohim, Yahweh and Lord, are also capitalized.
Again: specific gods (being names), capitalized; non-specific gods, not-capitalized.