There are two main explanations for how people think: one explanation suggests that thinking is totally dependent on language and wouldn't be possible without it. Another explanation takes the easy way out and says that thinking shapes but isn't absolutely responsible for what's known as thinking.
Personally I think it's more safe than sorry to assume that thinking has a definite and important effect on the way one thinks. There's so much variety in language, and being a foreign language learner I know that if I spoke another language as my native tongue it'd change who I was as a person. Different languages have different ways of saying and even seeing things than other languages. For instance, Chinese is a language that puts much more emphasis on the relationship's one has with their family, using more descriptive words for cousins, aunts, etc.
Anyway, I don't believe that thinking isn't possible without language. I do believe that all mammals have their own way of thinking, no matter how simplistic that thinking is. For example, when a dog is hungry it knows to go bother it's owner to get some food. How could a dog know to bother it's owner for food? Conditioning, sure, but how could conditioning be possible without thinking?