I am regularly shocked by how little imagination commentators in the popular science press seem to have on this subject. Even highly-respected scientists frequently refer to "requirements" for extra-terrestrial life such as carbon-based chemistry, the requirement for water, a mechanism of natural selection, etc, etc. (Actually I consider the last one, posited by Dawkins, to be probably the closest to the truth.)
I guess it's simply the anthropic principle at work, but even the nature we see on our own planet far surpasses our imagination often (especially at the microbial level), so why should we be placing any constraints on the rest of the universe?
Additionally, carbon itself forms stable amino acids, stable nucleic acids, and does so not only on Earth but even in celestial samples we have taken from outside Earth origin. So, would you rather a non-scientific writer leave the confines of sound science to speculate wildly? As a scientist myself, I'd rather they confine themselves to the most likely and sensible scenarios the majority of the time, since their purpose is to inform and inspire the public. Some small amount of speculation is fine, but education should be first and foremost.
Good answer though.
From there it probably gets a lot more divergent. I'd also bet that cells and something like DNA is pretty common wherever carbon-based life is found, but my understanding is that the exact way DNA codes for proteins is pretty arbitrary, and the fact that all life on Earth more-or-less uses the same coding scheme is an artifact of the common origin of life rather than because it matters.
Body plans and the details of multi-cellular life are probably going to be wildly divergent, with some caveats. For instance, eyeballs evolved multiple times on Earth, so it would be surprising if eyeballs didn't evolve pretty often elsewhere.
(Incidentally, if aliens are made of proteins, sugars/starches and fats, that means that whatever they look like, we can probably eat 'em, barring the usual toxins and allergens.)
So, you ask, what about Silicon? Silicon also has 4 valence electrons, so it ought to be a nice substitute, right?
The problem is that Silicon is in the next row down.. so it's more massive and it's electron cloud takes up more room. So you still only have 4- connectors, but it's a larger element.
There's clearly an advantage into being able to form precise and small molecules. Carbon, with it's small size and 4 valence electrons, is a clear choice for a backbone.
I'm a complete layman, but how does that play out in planets with gravity force significantly stronger or weaker than Earth? Woul that skew which elements make the best building blocks?
Silicon is basically impossible as a building block for life. It forms bonds that are too strong, meaning it requires much more energy to fuel life processes and reducing the rate of chance collisions which lowers the prospects for abiogenesis.
Carbon is the only realistic choice; it is the only element abundant enough with the right balance of stability and versatility.
Now it would be reasonable to say "well what about extreme environments" but we are specifically looking for planets with temperatures and "ambient energies" similar to ours - so it's reasonable to think that whatever chemistry is there probably has to follow Earth to a large degree.
If instead we were talking about high-pressure hot Jupiters or something, then it gets more interesting - but that's going to be something so different we're unlikely to recognize it at all (what consciousness does sentient life which evolved in a gas-environment have?)
That bond stability had to play a gigantic role over the last billion years of evolution.
And knowing that life like ours has already developed on a planet like ours, it makes sense that there will be others like it out there, so we might as well look for them first.
I'm not saying that ET life can't be very different to ours, or develop in conditions radically different to ours- but it makes sense to start searching at the most likely place for the most likely thing, no?
It may be the most likely to be easily recognized but not necessarily the most prevalent. You have two variables to balance: (a) likelihood that the planet you're looking at contains life and (b) likelihood that you'll know it when you see it.
If you can increase (a) significantly then it may not matter if (b) is very low or not
We'd have no way of identifying an earth-sized planet at an earth-sized distance from a sun-sized, star, as far as I know.
There could be a huge amount of exactly earth like planets out there that we have no way of finding. In fact -- all the sun-sized stars we've looked at that we can't find planets at all around, might be ones with solar systems just like our own.
But I am not an astronomer, would love to see some data on this.