There are many types of Exoplanet and life may be possible on some.
Hot Jupiters are Gas giant planets that orbit very close to their parent star. They are generally as close as .05 AU and have temperatures in excess of 1,000 degrees Celsius. Any terrestrial planets formed after a Hot Jupiter migrates into the inner planetary system would be particularly water-rich which would make life more probable. . Any planet formed before the Hot Jupiter migrates would be destroyed as the large Hot Jupiter crosses its orbit and collides with it.
Eccentric Jupiters are nothing to do with a mythological entity like Jupiter being eccentric.
In reality eccentric Jupiters are gas giant exoplanets that have eccentric orbits (that means the orbit of an eccentric Jupiter is highly elliptical and the distance of this planet from its sun varies at different places in its orbit). These planets generally throw out any planets of Earth-like mass. Earth like planets are the only planets that we know for sure can be life sustaining though planets and moons like Europa may be life sustaining as well.
So any planetary system that includes an eccentric Jupiter is unlikely to be life sustaining. 
Ocean planets are a hypothetical type of planet whose surface is covered completely by water. The oceans could be hundreds of kilometers deep and at the bottom, water could become ice because of extreme pressure caused by the ocean water on top. Waves might become kilometers high.  Ocean planets have been discovered and Scientists believe life is possible there. 
- On the formation of terrestrial planets in hot-Jupiter systems
- Eccentric Jupiter
- Evaporation rate of hot Jupiters and formation of Chthonian planets
- The Orbital Evolution of a Circumbinary Planet
- On the formation and migration of giant planets in circumbinary discs
- On the evolution of giant protoplanets forming in circumbinary discs
- Ocean Planets on the Brink of Detection
- Ocean Planet
- What Might Alien Life Look Like on New 'Water World' Planets?