I am familiar with some of them! I find associations really fun and interesting, even though I don't believe in astrological influences or whatever. Here are my stats:
Date of Birth: January 17, 1978.
Day of Birth: Tuesday--"Tuesday's child is full of grace." I like Tuesdays.
Zodiac Sign: Capricorn (bordering on Aquarius). Western astrology is fun to read the mythology about, and though my dad's side of the family has a running joke about the proliferation of Capricorns in our family taking over everything, I think Aquarius-related traits match me more often. I don't have any special affinity for the Capricorn "identity" or whatever.
Astrological Element: Earth. That's not my element of choice--I tend to "test" as an Air person--but I can appreciate the aspects of groundedness and practicality in Earth. I haven't always been the most traditionally practical of people, but as an adult I'm very good at planning, being realistic about how much time something will take and carrying it out, and managing my household.
Astrological Ruling Planet: Saturn. Saturn is way cool.
Astrological Color: Brown. I can roll with that! Not the most glamorous of colors but it doesn't have to be. I can make it look good when I wear it.
Astrological Animal: Goat. This obviously ties into the Capricorn myth. I don't know much about goats except they're agile, good at climbing, and will eat anything. So not at all like me.
Chinese Astrology: Year of the Snake, and my day sign is "Earth Rabbit." Some people mistake me as being part of the Year of the Horse because I was born in 1978, but the Chinese New Year is not the same day as the new year in the Western world, and by the Chinese calendar I was born in the equivalent of 1977. People born in Year of the Snake are intuitive, private, wise, good at communication, hate failure, prefer working alone, are easily stressed out, are materialistic, and tend to be enigmatic. There are supposed to be five types of snakes based on elements, and 1977 is a "fire Snake" year, which supposedly indicates a person who is smart, insightful, communicative, active, and fond of the limelight. I would say most of this is accurate, though I think I talk more than the mythology says Snakes do and am less enigmatic because I share everything about myself.
Birthstone: Garnet. WELP. I actually used to not really care for my birthstone much because it's very deep red and not particularly shiny and reflective--at least, in most of the cheap birthstone jewelry I had as a kid. I maaaaaay have developed a new appreciation for my birthstone since it's my favorite character on Steven Universe, but we aren't talking about cartoons right now. (For once.) Let's just say I would be much more interested in wearing garnet jewelry now, and the dark red color is pretty boss. :) Garnet symbolizes peace, prosperity, good health, loyalty, and enduring affections. Yes, I think those work for me.
Starstone: Black Onyx. It's supposed to stand for self control, decision-making, intuition, and protection. I can get with that--I like to think I have a lot of discipline and good decision-making abilities, and that I can be intuitive and protective.
Birth Month Flower: Snowdrop or carnation. Snowdrops are pretty white flowers that symbolize purity, hope, rebirth, and consolation/sympathy--seems like a funeral flower, but I like it better than the carnation, which symbolizes love, fascination, and distinction. Carnation's a nice flower honestly, but it's just kind of bulky and maybe a little on the garish side, while snowdrops are sort of delicate and humble.
There are probably other birthday-related symbols that I don't know about, but I'll end the list and analysis here!