Well, there is a measure of how a planet could be considered like Earth, called Planetary habitability. Based on this measure, what are the prerequisites needed to consider a planet to be a habitable one?
Habitable by whom? There are conditions that are uninhabitable by humans, however, many "extremophiles" survive perfectly happy.
Although, if you are talking about humans, here is a small list (all the rest are probably more "nice to have" requisites):
All this said, since we only have a sample size of one currently for planetary life, we really don't know what is possible, or how to bound the problem. ANYTHING is just speculation drawn from this one sample. That said, we have found life on our own planet where we never suspected it to be. Life has proven to be nearly unstoppable in propagating throughout every niche on this planet. So, the better question I think would be what are the requisites for abiogenesis? I think once life manages to start on any planet, it will adapt to whatever conditions the planet presents (to within a reasonable degree).
We have essentially one criteria for looking for planets that contain life: liquid water. This requirement covers planets that:
But that's just because the one trait shared by all life on Earth is that they need water to survive. We don't know what other kinds of life are possible, because we haven't found any on other planets.
But consider that all life on Earth requires water because that is pretty much the one condition that has remained constant through Earth's history (since the beginning of life). Conditions which changed caused extinctions and adaptations (such as the oxygen catastrophe) until we get to the present earth with most of its life drinking water and breathing oxygen. So if the earth could go from being oxygen-free to containing an abundance of oxygen which nearly all life requires to survive (a big change), maybe the water could have also been substituted for something else? After all, life didn't come from water, it evolved to use water as its solvent of choice because there was an abundance of it.
So maybe life is possible without water if it grew up in an environment without it. But how did life get started on Earth? Can we look for that on other planets? Actually, nobody knows. There are some processes we think probably contributed to the process (see the Miller-Urey experiment) which involve the presence of a few elements and some weather conditions. But we don't know the full process (we couldn't make abiogenesis happen in a lab, for example) and even if we did, it's unlikely we could look for that on another planet. We can't even really see other planets, aside from indirect data and small points of light. We don't know what conditions are necessary for abiogenesis, or how to look for it -- even if we find a planet which is nearly identical to Earth, there's no guarantee that abiogenesis happened there.
As far as we know, any planet could contain some kind of life. But to maximize our chances, we're only getting excited about earth-like planets since we already know the kinds of life which can exist there.