What made Kepler think that orbits are not circular which came to be elliptical? Kepler formulated his laws in a sort of time where human began to believe in heliocentric universe and telescope was not yet invented/ discovered. So what made Kepler think that orbits aren't circular?
 A: Here's a summary of what Malcolm Longair discusses in Theoretical Concepts in Physics. Kepler was assigned by Tycho to analyze the huge amounts of data he had collected from  about 20 years of observations. Tycho was interested in whether his hybrid model would fit the data better than the Ptolemaian (sp?) and the Copernican models.  they were notoriously poor in describing Mar's orbit. Tycho's model had the Earth at the center with the Sun and Moon orbiting Earth and the other planets orbiting the Sun, all in circles.
After extensive analysis, the Mar's data would not fit circular orbits. Tycho had analyzed his systematic errors very carefully. The huge amount of data gave Kepler a tremendous sense of the non-systematic (statistical) uncertainties, and these were very small compared to other data sets (a factor of 10 smaller).
Kepler was a big believer that data told the truth. After circles failed, he began using other closed curves (ovoids) and finally found (with lots of analysis) that an elliptical path for Mars with the Sun at a focus and a circular path for Earth gave an excellent fit for the data.  The reason that worked (with the Earth being circular) is that Earth's eccentricity (0.0167) was too small to show up in the data while Mar's eccentricity (0.093) was large enough.  Kepler then tested other data which showed that ellipses could be used for all the planets.
While using an ellipse was quite a leap (even Galileo wanted the path to be circular even after Kepler shared the results with him), a bigger leap was to try the Sun's location at a focus and not the center.
A: In respect to above answer, although you are correct but there is a little discrepancy in your last line " a bigger leap was to try the Sun's location at a focus and not the center."   
A circle is a ellipsoid with a special case having the two foci at same point, so there could not be so chance putting in centre because it was observed that planets near sun orbited fast than when they were away from sun, from which Kepler concluded that the "line joining any planet to the sun sweeps equal areas in equal intervals of time."
