The other answers here so far are philosophical, I'll give you one that's scientific. Most of the biochemistry of life is required just to have life at all. The incremental increases in complexity of the biochemistry for complex or multi-cellular life is relatively modest. Therefore you get most of the bang for your biochemical buck just by having life at all.
Because it poses new interesting questions: If extra-terrestrial life exists, do we have a common ancestor? This is the theory of panspermia. Or does life spontaneously arise when conditions are right, but with variation?
It would be particularly exciting to discover life that is similar to Earth but with an opposite chirality, or a genetic code that encodes amino acids using different base pairs.
I am willing to bet that whatever is eventually found will be remarkably similar to what we are familiar with on Earth, assuming a liquid-water environment, and the constraints that implies. Single-celled life appears to have arisen so rapidly that it predates the end of the Late Heavy Bombardment, after all.
(I'd be thrilled to be wrong about this, of course, just as I would be fascinated with any xenobiological discovery at all. But I do think the 'endless forms most beautiful' are also strongly constrained by simple physics, and thus the solutions found by an evolutionary random walk will resemble what we already know.)
This is what I suspect with microorganisms as well. Macroorganisms are much more complex and they have common features that seem very arbitrary like moving via cylindrical appendages called legs, or having faces that feature 2 eyes, a nose, and a mouth. It makes me think that it's much more likely to see something wildly different between macroorganisms on Earth and elsewhere than between microorganisms. It would be cool to see other forms of movement, other forms senses, other forms of communication, other forms of anatomy, etc.
EDIT: It also makes me wonder how different an ecosystem could be. Imagine one that did not require macroorganisms eating other macroorganisms, like ones that feed on heat or wind.
EDIT 2: Maybe mating requires 3 genders, etc. There seems to be a lot of room for variation.
There's even wild differences between macroorganisms
on Earth.
Invertebrates are much more relaxed about number of eyes etc.
We can go from "humans are the optimal form!", to "well, some kind of mammal", "c'mon, it's got to be a vertebrate", then get into the Cambrian experiment, go back further to different DNA (RNA anyone), then to different metabolic pathways, then to different organic biochemistry, then to non-carbon... and why should life have a chemical basis, anyway? So chemocentric.
How can we tell when he go from too anthropocentric to too anti-anthropocentric? We have guesswork only. We're like a child rebelling against its parents.
It seems to me, that elephants, dolphins, parrots, octipuses, and even spiders could have undergone the rapid brain-size increase that happened to some apes. (We don't even know why it happened to us.) They might still do so, in a few million years.
On the other hand, some physical features have evolved multiple times independently. The eye is one key example. IMO this is a strong indication that creatures that evolved in places other than Earth probably also have something we'd recognize as eyes.
Note that some earth creatures - deep sea and underground - have almost lost eyes. Like [blind mole rats](https://wikipedia.org/wiki/Spalax). They have appropriately alien-like nose-antennae.
The rapid emergence of single-celled life on Earth is not necessarily evidence that it was an easy step for evolution. See the discussion surrounding “conditional on success, all the hard steps, no matter how hard, take about the same time” in this article: http://mason.gmu.edu/~rhanson/greatfilter.html
