We can’t think of a single good reason why it shouldn’t, if the conditions are right!
The hardest part is getting the right conditions. On Earth, the biggest requirement for life is water. Our planet is very good at growing things in every possible location, so long as it’s near or in liquid water. Life arose extremely quickly after the formation of the earth, which seems to indicate that if once the Earth had a surface with liquid water on it, there were not a lot of other stumbling blocks to overcome before life could spring forth.
Having liquid water usually means that the planet has to be in a relatively narrow distance window away from its star, and have a surface upon which the water can rest. Effectively, we need rocky planets at exactly the right distance from the sun such that all the water doesn’t freeze solid or evaporate away. Outside of that distance band in a solar system which allows for liquid water, there are precious few opportunities for liquid water to exist, except in unusual cases like Enceladus, a moon of Saturn, and Europa, a moon of Jupiter. Both of these moons are thought to have an ocean of liquid water under their icy surfaces. These small moons can maintain liquid water because the tidal forces from the massive planets they orbit are constantly stretching the rock at the cores of the moons. This stretching heats up the rock, and that heating provides the energy required to maintain liquid water, even though these moons are far too distant from the sun to keep liquid water on their surfaces. As a result, planetary scientists are very excited about the prospect of being able to find life on Europa and Enceladus, but in order to go check, we’ll have to send a craft to those moons to look directly.
Also within our solar system, we are currently looking for evidence that life once existed on Mars. The information coming back from our Mars rovers tells us that Mars was once warmer and wetter than it is now, which means that it should have been a good place for life, back when it was able to hold liquid water. However, since Mars has become very cold over the years, we don’t expect to find evidence of life currently thriving there.
Looking for planets outside our solar system becomes much more difficult than looking within it; for starters, it’s much more difficult to find the planets to start with. We then need to filter out only the ones that fall within this magic range of distances from their star where liquid water can exist. The technology to find rocky planets in the liquid water zone has only recently been developed. These planets are extremely hard to detect, and push the boundaries of the sensitivity of our telescopes. The Kepler satellite has begun to push into this realm of extrasolar planets, and the massive amount of data it took before the end of its mission is still being analyzed. It seems, from the data that’s been studied so far, that about 20% of all stars like our sun have a planet around it like the Earth - a rocky planet near enough to the star to have liquid water.
Proving that liquid water does in fact exist on those planets is more difficult still - you have to detect the signature of water in the atmosphere of a planet that is light years away. Proving the existence of life will be an even more difficult task, but once we begin to find lots of planets with liquid water on their surfaces, the odds are pretty good that one of them will contain life of some form. It will be much easier to search for life within our own solar system, since we can actually go to these places and see what’s there directly.
No matter where it might be - the search is on.