Most of my experiences of thinking without language involve either emotions or sensory input memory.
I am reasonably sure that my emotions can run without language because I've had emotions that I don't have words for in any language I know. One grew so bad I had to give it a name so I could talk about it, but I couldn't explain it in plain language at all until I read some of Anna Wierzbicka's work on a Natural Semantic Metalanguage. (Analyzing it helped me explain it. It's noded at frath.)
I'm also rather sure that my sensory memory doesn't invoke language because, of course, a great deal of our senses aren't hardly begun to be defined in language--what does that smell like? What does that taste like?
(Just a little something for the proponents of the strong Sapir-Whorf hypothesis, which I'm otherwise in favor of.)