When you come home to your house after a longer period of being away, there is always that special smell in your house which you can’t usually smell (the smell of the house) because you’ve gotten used to it over time. That made me wonder if the same thing applies to Earth, which is our home too.
It may be a weird question, but is it possible that planets have their own unique smell that one would get used to over time if they were inhabitants of it?
What’s that smell, the smell of outside, that clings to you when you come in from outdoors? That must be it, the smell of simply being on the earth.
Of course. It smells earthy. I don’t know why you think we can’t smell it, though.
That is not what I meant. What I meant, was if you sense a different smell on Earth if you would leave for a longer period of time and then come back. Your house never loses its smell entirely, regardless of how long you have lived there, but if you leave and come back, the house has a completely different smell for a while when you come back.
When we lived in the Houston area and returned home after a vacation, it was always nice to be greeted by a welcoming fragrance* as we stepped outside the airport terminal
*compounded of heat, decay, fungus and a subtle overlay of petrochemicals. 
The Moon apparently has a distinctive smell: The Mysterious Smell of Moondust | Science Mission Directorate
(I guess that’s the same smell you can feel when you pound a piece of rock with a sledgehammer.)
Just LA and New Jersey.
You smell because you have receptors in your nose hooked up to neurons in the brain to receive signals from the receptor. You don’t have smell receptors for oxygen or nitrogen, but if you did, you would smell them. There are receptors for CO2 but they are not connected to the olfactory area in the brain, but to the breathe area. Of course, different locations might trigger smells. The salt-water smell is not of the salt, but of various odors coming out of the sea. Freshly mown grass is another.
Different soils have different smells. (Farmers may be more likely to notice this than most other people in this society.) So I’m dubious that the planet as a whole has a specific smell; though specific locations certainly do.
What I think is the underlying question here is one I find really interesting, though: what are the things that we in general, or I as a specific person, aren’t noticing because we’ve never been without/outside them? And how does one become aware of something that one’s not aware of?
Given that different places on Earth have drastically different smells, I doubt that there is a general “Earth” smell that we are accustomed to. Deserts, pine forests, tropical forests, and open ocean all have distinct smells that are very different from one another. The “background” gases that make up most of the atmosphere, nitrogen, oxygen, argon, and carbon dioxide are odorless to us.
That’s not to say that different planets wouldn’t smell drastically different if you were transported there. I think on Jupiter that you would detect a strong odor of ammonia and hydrogen sulfide (in the brief seconds before you died in agony).
One of the very few things that humans are extremely good at - smelling petrichor. 
From the linked article:
Of course, planets have distinct smells. This will be the basis for Professor Hubert Farnsworth’s invention of the Smell-O-Scope in the year 3000.
What OP is (in part) referring to is habituation, a reduction in response to persistent presentation of a stimulus.
But you also have to consider the evolutionary context. As Colibri points out, “Earth” is not one smell. There has obviously been no explicit selective pressure to distinguish between planets, but rather to distinguish (to whatever extent) among different smells that we encounter on earth. Still, given that we can distinguish a wide variety of smells, a strange planet would probably contain many distinctive smells that we could recognize; and habituation would certainly reduce our sensitivity to those smells if we lived there.
Oxygen. You know how recognizable ozone smells? To someone not used to breathing it everyday, our planet must smell horrible
Someone’s been reading Asimov.
Cape Canaveral probably doesn’t smell much like Baikonur does. My guess would be that one part of the Moon smells like any other, and perhaps the same is true of Mars. But I would guess that the humid subtropical zone of the coastal areas of the western continent of Teegarden’s Star b don’t smell much like the central steppes of the eastern continent (optimistically assuming that such places as “the humid subtropical zone of the coastal areas of the western continent of Teegarden’s Star b” even exist).
I wonder if the north polar lake country of Titan would smell different than the equatorial dunes, to some organism that was equipped to not freeze solid and asphyxiate in the Titanian atmosphere?
The moon, according to the astronauts who went there, smells like spent gunpowder.
Edit: Bah, I see Ignotus beat me to it.
My food-science friend gave me a taste trial with sample of frozen sweet-n-sour chicken. One had been frozen 3 days: one had been frozen 6 months. Not only could I taste the difference, I immediately recognized the flavour of the 6-month sample. But then it was gone again: I hadn’t learned it well enough to remember it. Unless I have the two sample side-by-side, I can’t identify the flavour associated with flavour degradation due to long-term frozen storage.
My new favorite word!
It;s not quite the same as an “earth” smell, but I’d read that sailors could sometimes smell land as they approached it. I had this experience while living on the island of Pohnpei - we’d gone out on our boat for several hours, and as we approached land, I could smell it - it smelled of plant life. A wonderful, heady scent.