I have sometimes heard that Siddhartha Gautama's philosophy was influenced by Cārvāka system of philosophy. Is this true, and if true, to what extent has Cārvāka system influenced Buddhism?
I would like to put a slightly different view to Suminda
Although the Buddha was undoubtedly a hugely original innovator (to say the least) I think it is fair to say that he was also influenced by the philosophical and spiritual environment of Northern India at the time. He would have been influenced by the Jains, The Brahminical traditions, the Sramanas and by other philosophies such as Cārvāka. However the influence of the philosophies could have been as much reacting against as inspired by. In the case of Cārvāka the influence could have run both ways.
The Cārvāka system might have provided the extreme of nihilism (or annihilationism) that the Buddha was reacting against when he proposed the Middle Way. The other extreme of eternalism would have been more characteristic of the Brahminical traditions.
More positively, the Cārvāka system could have influenced the Buddha in his skeptical stance to questions unrelated to liberation i.e. his refusal to answer questions on the fate of the universe or what happens after death. The sort of skepticism shown by the Buddha would have probably been of the weaker kind though - one of suspension of judgement rather than the absolute impossibility of knowing. Interestingly the Greek skeptics could have been influenced by Eastern philosophy through figures such as Pyrrho. So Cārvāka might have also influence the Western philosophical tradition either directly or perhaps via transmission through Buddhism.
Just as an aside I've written a bit more on the influence of Buddhism on Western philosophy here. Also this question goes more into the relationship between nihilism and Buddhism though we didn't mention Cārvāka. Maybe we should have.
The Buddha claims that what he is about to teach is previously unheard of. Hence I double that there were any material influences on the core of Buddhism though he did draw from existing customs and techniques which were appropriate. E.g. Sila, some of the Samatha meditation techniques, etc.
Buddha rejected 62 wrong view of his time. Ucchedavada proposed by Ajita Kesakambali, one of the earliest Cārvāka thinkers, was also rejected by Buddha among other. These views arise due to theorising and philosophising without going to the pinnacle of understanding or realisation of the ultimate truth. Hence there cannot be any perceivable influence from this doctrine.