Better than Earth habitability Earth undoubtly has very good conditions for supporting life. Although it is expected that many other planets on the outer space have conditions at least as good as Earth, the vast majority doesn't, making them unhospitable to life or probably being able to support only very simple lifeforms. Earth itself for some billions of years until the Ediacaran or Cambrian could only support very simple lifeforms.

There are many parameters that may influence the habitability of a planet and its ability to support complex life: Star type; star temperature; star luminosity; stellar activity; stellar stability; star age; planet age; planet composition; planet size; orbital excentricity; orbital length; rotation axis inclination; planet tectonics; planet magnetosphere; presence and influence of satellites; abundance of water; planet atmosphere; interactions with other planets; presence or absence of asteroids, comets and minor planets planets belts and their position, distribution and composition; galactic orbit; galactic neighborhood; mass-extinction events rate, probability and intensity; and hundred of other possible variables including some based on pure luck and random chance.

Many of the parameters are modeled after Earth itself, since Earth is the only place so far that we know that life exists, and even if we found some alien life somewhere, it will probably be limited only to very simple forms of life.

But, what combinations of those parameters could lead to a planet with better life support than Earth itself?

Ok, you may argue that the question is too broad, so by "good life support" we could say something that allows the planet to evolve plenty biodiverse multicellular life ranging from simple microscopic creatures to complex dozens-meters long creatures with many body-differentiated parts and organs in a short timespan. So, a planet that has an environment which allows the development of richly-diverse and complex plant-like and animal-like creatures in a billion years after formation and stay like this for another 10 billion years is expected to be more life-friendly than Earth.

Further, lets restrict the biochemistry to what we know: water-based and carbon-based life, but not necessarily oxygen-breathing.

By the way, I am not asking anything about intelligent life or humans, just complex multicellular and biodiverse life.

By the way: two important links about the subject: http://www.nature.com/scientificamerican/journal/v312/n1/box/scientificamerican0115-32_BX1.html and http://www.nature.com/scientificamerican/journal/v312/n1/full/scientificamerican0115-32.html
Note: I am self-answering my own question in hope that someone post another answer that beats this one.



Earth is near the inner edge of the Sun's habitable zone. And since the Sun is expected to grow and increase it luminance, Earth might be unhihabitable for any life somewhere between 1 or 3 billion years in the future. So, a planet that have longer time to develop before its parent star moves it beyond the inner edge of the habitable zone is more favorable than Earth.

Since Earth itself always was inside the habitable zone since it formed 4.6 billion years ago and will still be for lets say more 1.4 billion years, with a large uncertanity factor, this gives roughly 6 billion years of time for complex life to develop. Given that it is unlikely to form early due to the time needed for evolution to take place and due to an elevated level of large bollides collisions, we could discount the first 2 billion years from any life bearing planet, including Earth, as unlikely to develop complex life. Further, it is unlikely that complex life would finally evolve out from simpler forms when the planet is already overheated and already crossing the inner edge of the habitability zone, so lets take out the finishing 10% of that period for any planet (probably something more than 10%, but lets keep this as a conservative estimative). So, for Earth, this gives a window of a size of 3.4 billions years to complex life evolve. Similar planets with larger windows have better probabilities. 

Stars larger and more luminous than the Sun tends to be more unstable and live shorter. As a result, it is expected that planets around stars larger than the Sun has less time to develop complex life, and thus a shorter time-window. On the other hand, this means that stars smaller and less luminous than the Sun gives a larger time-window to the planets to develop life.

For stars smaller than the Sun (a G-type yellow star), we could consider the K-types (aka, orange dwarf) and the M-types (aka, red dwarf) as specially favorable.
An orange dwarf star may live for 10 to 30 billions years in the main sequence. A red dwarf star may live in the main sequence for trillions of years.

However, planets in the habitable zone of red dwarfs are likely to become tidally lock, and we don't know if this is really that bad or not for life biodiversity. Lets assume that this is really bad, so a planet orbiting an orange dwarf in the habitable zone is likely to have a better habitability than Earth.

Accordingly to this, a planet with two times the mass of the Earth, will have stronger gravity, and thus it is likely to be flatter. Further, it is likely to have a ticker atmosphere that would protect the surface from UV radiation better than Earth. It would be geologically active for a longer time, resulting in more carbon cycling. With the right quantity of water (not a desert nor a global very deep ocean), it might be an archipelago world, since its flatness would not allow the ocean to be very deep nor the continents to be very large. As a result, life would flourish in a number of rich biologically favourable environments significantly larger than Earth. Further it magnetic field is likely to be stronger than Earth's one, protecting the surface from cosmic rays.

As a result, a planet with two Earth masses orbiting an orange dwarf star in the habitable zone has a good chance to be more habitable to life than Earth itself.

Needless to say, near-circular orbits are more favourable than excentric ones, since excentric orbits may make the planet enter in periods of freezing or boiling. However, a reasonably excentricity that periodically changes the environment in a significant manner, but not as too much that it would extinguish non-extremophile life, might give to the planet life a selective pressure needed for developing rapid evolution to face the always changing climate.