I think that there is something you can say reasonably definitively. That if we continue with exploration of astrobiology then we are pretty much bound to find something interesting about this question.
So, either
1. We will find life on other planets (including dwarf planets, or moons in our solar system) or 2. We will find out that life is very rare in the universe.
In case 2. then we will also learn a lot about what happens to a planet with apparently all the conditions for life, but where life doesn't develop.
E.g. do you get RNA, and DNA but no life? Some theories of abiogenesis suggest that RNA may form rather easily. Well if they are right, presumably we will find deposits of RNA on other planets in our solar system. So that would be replication but only chemical, rather like a growing crystal, without life as we would understand it.
Others think that the metabolism came first. If so presumably we will find evidence of metabolism without replication.
Any discovery like that would lead to great increases of our understanding of the origins of life.
We might also find organics on the Moon brought there by meteorites from early Earth.
In case 1. then I think in many ways worst case is that we find that the life in our solar system all has a common origin with Earth life through meteorite transfer.
Because then we don't learn too much about the origins of life, though we might still be able to find protocells and evidence of the early stages of evolution in very early deposits not yet "contaminated" by modern life. Frozen below the surface on the Moon, Mars, or some icy moon some ancient fragment that has been cryopreserved from the early solar system complete with organics and the earliest forms of life. After all back then we think there was life on Earth and also many huge giant meteorites hitting Earth - some of that life must have been thrown into space and ended up on the Moon or on asteroids and been preserved, if we know where to look (scientists have suggested the icy poles of the Moon could be a good place to start to look for it).
If the life is all related though, chances are that most of the interplanetary transfer happened in the late heavy bombardment, way back in the first few hundred million years of our solar system - especially for the outermost moons. So that would be long before the earliest evidence we have of life on Earth. So, still we might push back the earliest common ancestor, and though still based on DNA chances are, it might still have radically different cell organization or - things like a new type of photosynthesis (we have basically 2 mechanisms for photosynthesis - the green chlorophyll approach, and the approach of the halobacteria which are red instead, and generate energy from light using a similar method to the method we use to see with our eyes - with 2 mechanisms, may there be a third or a fourth explored somewhere else in our solar system? )
Or what about the very earliest forms of life, they must have been smaller than modern cells, say a few tens of nanometers across, too small for all the machinery of modern life, so maybe we find evidence of those, still surviving somewhere in our solar system. Maybe reproduce only imperfectly.
Or, most interesting case, is we find life that has evolved in a different direction right from the start. No common ancestor at all. If we find just one other example that would be huge in its implications.
Anyway as David Frost said, we have very capable instruments now. It depends on political will a fair bit. But we could send ice moles to explore Enceladus and Europa. We will surely be able to examine a comet close up as Philae hopes to do - if it wakes up it will tell us a lot about organics on comets, precursors to life probably. If not, surely some future spacecraft will. And on Mars there are many interesting habitats to explore. And on the Moon, searching for meteorites from ancient Earth, maybe in the polar ice deposits with the organics preserved.
So, I don't think you can possibly say for sure that we will find evidence of life not evolved from Earth. Rather, that's the open question that motivates all this, and it wouldn't be a question if we already knew the answer.
So, that's the big question, how common that life is, how easy it is for a "second genesis" to happen, and is it so common we have a chance of finding it in our solar system?
I think myself there is so much focus on searching for life, sometimes people forget how interesting it might be to find a planet without life, but with precursors that are "almost alive" but didn't quite get to the present capabilities of life. We would dearly like to have some extra data points between lifeless chemicals and the fully evolved modern cell. Either on the same line of development as modern life or a separate line.
And I think there is a reasonable chance of that, either that or independently evolved life, or at least, DNA based life with different capabilities from Earth life. Must be something in the seas of Europa and Enceladus, and in the deep hydrosphere of Mars if it exists, and the various possibly habitable micro-habitats on Mars if they exist. Is it life? Is it protolife? Is it just a big ocean of organics, complete with hydrothermal vents, but no life ever evolved for billions of years? If so - what kind of complex chemistry did evolve, and can we somehow begin to get a handle on why it didn't evolve into life?
Well we should find out some time in the next few decades.
We have to be careful though, while exploring, that we don't just find life that we brought to these various places ourselves on our spacecraft, and with current technology, that's quite a major challenge to achieve that level of planetary protection in the complex and capable spacecraft that we want to send to these places. Especially for the subsurface oceans which potentially may be a very habitable environment for any Earth life stowaways on our spacecraft.
I've put more ideas about this into the comments to keep the answer focused and not too long.