This is your friendly neighborhood cognitive science fanatic - this question is poorly-worded, because it is asking about thought in general, when it is fairly obvious to most observers that animals think. What is meant, more likely, is to ask whether human thought is possible without language. This is a variation of the Sapir-Whorf Hypothesis, which posits our language affects how we think about things - e.g., if we have more words for shades of blue, especially ones thay conceptualize them as totally different colors, then we will be more apt to differentiate between shades of blue.
In this sense, it is difficult to deny that human language influences thought. Look up Japanese street lights; color naming differences between Japanese and English have led to a fun postwar phenomenon in that the color of their "Go" light on traffic lights - normally green as an American would think of it - is in fact rather more blue...
But all that aside, if one has no language, can one have concepts equivalent to those of a linguistically-gifted individual? This is a more difficult and freighted question. As others have intimated, Pinker believed an underlying "mentalese" was built in to the human brain, providing a structure - a computational architecture, if we feel like pleasing the Functionalists - on which other languages were built and to which a mind fell back if no natural language was known. Problematically, we are left to determine what exactly the benefit of layering natural language over mentalese has for us, but perhaps it is an extension of the need to express thought externally which gives rise to the otherwise superfluous languages.
The alternative is to suppose that there is no language or protolanguage at all in the human mind, and that our language is fully a synthetic creation, which would mean thoughts prior to language learning would be by definition without concept - simply the apprehension of raw stimulus by a conscious mind, as perhaps a mouse might. This has its own problems, one of which is it doesn't explain how humans are so universally good at language.
I tend to fall into the prior camp. Part of this has to do with how difficult it ends up being to rigorously define "language" - much as we may conceive of nigh any set as a system, we may conceive of any system which we derive information from to be a language. It therefore seems likely that on some level, we are always thinking using some sort of "language."
I will close, however, on a quote from Helen Keller that has always fascinated me. She said of her preliterate life that it was:
"...a conscious time of nothingness. I did not know that I knew aught or that I lived or acted. I had neither will nor intellect. . . I had no power of thought."