Could the oracle really see the future or just predict choice based on human emotion?

In Matrix Trilogy, Oracle is kind of a dubious character. In first movie she is shown as a very knowledgeable woman whom few humans (like Morpheus) consults and believes in. Later she is revealed to a be program, residing in the core of the Matrix. She lacks the ability to see past her own choice, which explains that no one can see past their own choice they do not understand.

Oracle's power of foresight is not based on knowledge of a "pre-determined" future, but rather a calculation; Reason of Oracle's existence is simply to "investigate the human psyche", as mentioned by the Architect, allowing the Matrix to become more like a human world for humans to actually accept it.

Oracle actually predict events directly relevant to both programming of the Matrix and human responses according to her knowledge about them. Most relevant example is her prediction of Neo's choice between Morpheus' life and his own.

While the Oracle knew that the Agents would be searching for Morpheus as he was searching for 'the One', and seeing Cypher's actions and reactions (such as his conversation with Agent Smith), she predicted the most likely event.

Another example is her prediction about Neo's choice in The Matrix Reloaded;

She had existed throughout five versions, and regardless of the One's ability to exhibit free will, she had experienced a series of events that had and would occur and push the One to the Source.

So it can be concluded that her responses (predictions) are direct result of precise calculations of nature of the Matrix and her knowledge about human beings.

Further Information: Wiki