Malleable, inert, readily available to extract.

Basically things have value because we, as a society, deem them to be of superior value. If we had different needs and wants then the value would be different. One thing about gold that really bugs me is that whenever things are politically heading for a downturn for political reasons the value of gold goes up and every one who thinks they can get rich buys in, factually the economy goes back up and those who can well afford to loose, loose as the value they thought they had plummets. Basically if the pundits tell you to buy, don't. If the value was going to really go up and money was to be made they would not want to see it. Remember someone owns the gold you are going to purchase, the only reason they would want to do this is because they know they can make money from the sale. That money comes from those who think they know better.

Other than its physical properties, it's no more valuable than dirt. However, I have to confess that I've taken advantage of the natives a time or two. Gold coming out of our claim was about 35% flake and dust. During that time, gold prices and sales were still government controlled so the price ranged from $35.40 to $41.00 per ounce, but we were allowed to sell a portion of our 'reported' take for what was commonly called jeweler's gold for whatever we could get on the market. Dealing through actual jewelers kept the price down to around $120.00 to $180.00.

We found a source for bezels that would accept a double watch crystal (the old fashioned roundy ones) 5/8" dia. that were super cheap in bulk. These we would hawk to the natives rolling along the highway on their vacations from some of the lower forty-eight. It's amazing how the value jumped up there into the stratosphere. For our $5.00 investment in 0.10 ounces of flake/dust, bezel, and crystals, they were willing to part with $35.00 worth of paper money. We figured the natives knew something about gold that we didn't. Some of them even bought a mix of gold dust and black sand at an even better profit margin.

I don't know apart from being a fantastic conductor, I find it quite dull and would rather where stainless steel any day.

I don't see any logical reason to want gold other than to have something that never can loose all it's value. It is intriguing to hold a peace, but I can't say why.

It doesn't tarnish and is easy to shape.

It is bright and shiny and does not oxidize or corrode. A gold coin on a Spanish shipwreck in the Carribean will be as shiny as the day it was minted. It can be hammered into thin sheets to allow for gilding intricate forms which will stay shiny indefinitely.

Gold is relatively rare. There are about 187,000 tonnes above ground, so it is finite
It is a great conductor, very malleable, doesn't react with most acids, and looks wonderful around my wrist.

the top of the Washington monument was Aluminium, very rare at the time

what's more irrational is the value of diamonds. generated by nothing more than old fashioned commerce. Diamonds at a girls best friend?

The aliens that bio-engineered human beings for slave labor had humans mine it, so it's in our DNA to want gold!

(Just a joke)

it doesn't rust

There have been several attempts at displacing the "Gold Standard". Most notably with silver.
I referenced the Presidential Election of 1896 in a recent post. That same election, between republican candidate, McKinley, and democrat, Bryan, had at issue whether to change the Gold Standard to Silver. McKinley and the Robber Barons of the Gilded Age, were in favor of keeping gold, Bryan and the democrats were trying to change it to silver. Money won out, and McKinley became President.

Because it is beautiful and it doesn't get all crappy like silver.

Rarity, and prettiness. Then later industrial value... Mostly though rarity and prettiness.