As a snake impaled, I am not free.
Rather, I am displayed for all to see.
Why do people not mourn me?
Instead they want more of me.
You want more?
Four is my door.
Who am I?
note:
I added 2 lines to the riddle.
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The dollar sign. The $ looks like a snake impaled, displayed in front of all dollar amounts, is not mourned for contributing to one's wealth, and of course, people want more. "Four is my door" tipped me off, where it refers to the number 4 on the keyboard having the dollar sign as its shift-text.
Is it perhaps a
Belt?
A belt is sort of serpentine. It's "impaled" by prong which fastens it, so it's not free. Belts are worn visible to everyone. No one mourns them. There's a demand for them, since people buy them.
Is it a
Wrist Watch (with leather strap)
As a snake impaled
Has pierced holes to insert buckles in leather starp.
I am not free
Tied to the wrist
Rather, I am displayed for all to see.
Displayed for all to check time
Why do people not mourn me?
We won't mourn when the watch is dead
Instead they want more of me.
Instead we repair, or buy new batteries to run it again
First idea I could come up with:
A ring. The idea stems from the explanations of other answers: snake impaled may refer to the finger going through the center, it is worn to be shown off and displayed. The ring is often a symbol of celebration, as opposed to mourning. And of course, rings are worth something, be it sentimental or what have you.
As for the hint, "4 is my door", he refers to the fourth finger, also known as the Ring finger, where a ring is most commonly worn.
How about:
Pharmacy logos?
http://upload.wikimedia.org/wikipedia/commons/d/d9/Bowl_hygeia.svg
1 - Bowl of Hygieia, the internationally recognised symbol of pharmacy (the profession).
or this one
http://upload.wikimedia.org/wikipedia/commons/1/19/Asclepius_staff.svg
2 - Rod of Asclepius, the internationally recognised symbol of medicine.
As a snake impaled, I am not free.
Although the snake entwines in the classical explanation, it's rather ambigous in the logo (2 dimensional images, especially monochrome, often suffer from difference in 3 dimensional topological interpretation).
Rather, I am displayed for all to see.
Logo displayed on pharmacies for all to see.
Why do people not mourn me?
Dude your a picture, calm down.... :)
Instead they want more of me.
Helping and getting helped by others is considered to be a good thing.
You want more?
Yes
Four is my door.
The Chinese, Vietnamese, the Korean and the Japanese are superstitious about the number four because it is a homonym for "death" in their languages (wiki). So with death at your door or four being the next door (as in option to choose from), you go to the pharmacy (or infirmary).
or something like
Four is the number of classical elements (earth, water, air and fire). These elements are the root for alchemy, which is the root or predecessor of chemistry. (Maybe my last point is a little bit far fetched, but whatever.)
Are they,
Animals in Zoo
As a snake impaled, I am not free.
Animals kept in a cage.
Rather, I am displayed for all to see.
They all kept for us to see.
Why do people not mourn me?
People do not mourn if any of animal dies.
Instead they want more of me.
Instead we want more spices of them to see.