It isn't clear how much ability people have to think without language. Some people report having running monologues pretty much constantly, but others do not.
There are also a handful of famous cases of people who grew up with little or no language exposure. The most widely studied example is probably Genie. Another well known example is Ildefonso, described in Susan Schaller's book "The Man Without Words". Ildefonso was a deaf child who grew up in an environment where his parents had no way of communicating with him. He wasn't exposed to sign language until he was already an adult. That example makes one understand how people in ancient times considered deaf-mutes to be effectively stupid and crazy, although it isn't completely clear if that's due more to the lack of communication or the lack of language. In the case of Ildefonso, the story goes that when he realized that objects had names in sign language he burst into tears at the revelation.
Language is a very basic part of human thought processes. In order to do almost anything of note we need to be able to use language. I'm not at all convinced that developing ways of "thinking without words" is at all productive.
Language is useful. (Though it would be less so if people didn't automatically assume being nonverbal made you completely stupid. Picture boards!) It doesn't follow that we have to think exclusively in words. Language is not a very basic part of Amanda Baggs's thought processes, for example.
Thinking without words is useful because it's (sometimes) fast, and has different constraints.
Before language, people must have thought without words. I often have the impression that I have a thought fully-formed in my head, yet I wait to listen to it unfold in words before moving on to the next thought. Perhaps I could think much faster if I weren't addicted to words.
Has anyone developed techniques for thinking without words?
This would have a little in common with Buddhist practices of emptying your mind, but wouldn't be the same thing. For one thing, Buddhists also try to empty their minds of images. More importantly, they are trying not to think, while I'm trying to think - just not unpack everything into words.