Do Japanese state that they 'don't think' something as often as we do in English. E.g. I don't think I'd like to go there = あちらへ行きたいと思いません
I don't think I can do it = 出来ると思わない
I don't think it was very good = そんなに良かったと思いません
Would all those pass as normal sounding sentences in Japanese, or are they too 直訳?
Traditionally, "think/don't think" (思う・思わない)was not used very often in the Japanese language. However, the language has evolved, and this usage has become frequent today. So, there is no need to worry--basically.
As Supervin mentioned, the use of と思う to state a general opinion (on political issues, for example) is OK.
However, there is slight difference in usage for the examples you gave.
* I don't think I'd like to go there = あちらへ行きたいと思いません
Correct me if I'm wrong, but I think the English sentence suggests that you are being careful or courteous in stating your preference. On the other hand, the Japanese sentence is a more straightforward statement, saying in effect that "I don't want to go there."
To soften this, you can say:
あちらへ行きたいとは思いません。
(Implicit suggestion: I don't want to go there--but, I might agree to go somewhere else.)
あちらへ行きたいとは思えません。
(I cannot make myself want to go there.)
Personally, I would go for a more cautious approach:
出来れば、あちらへ行きたくありません。
行かなくて済むのでしたら、ありがたいです。
Similarly:
I don't think I can do it = 出来ると思わない
出来るとは思いません。
出来るとは思えません。
Preferred: 私に出来るようには思えません。
I don't think it was very good = そんなに良かったと思いません
そんなに良かったとは思いません。(This statement of opinion is still too direct in my opinion.)
そんなに良かったとは思えません。(This is reserved and less likely to hurt someone's feelings.)
Preferred: そんなに良いようには思えません。
HTH!
