You can use it to say "I think/believe so" to express your opinion but implying that you are not very confident.
In another situation, it is used as a question with the "ka" at the end skipped, provided that you raise the tone at the end.
Sou da to omoimasu? (Do you think so?)
Also:
I thought that movie was interesting.
Sono eiga ha omoshiroi to omoimashita.
"Omoimashita" already makes the sentence in the past tense.
However, I think this sentence is not natural, although grammatically correct. A more direct "sono eiga wa omoshirokatta [desu]" sounds better.