Is sign language pretty standard the world over? If it is, why aren't we all taught it?

No, unfortunately it is not. BTW it is a language in the sense that it is governed by the same innate rules (N. Chompsky´s idea) that spoken languages are. learn it more easily when young etc.

Nonetheless, each sign language is based upon the spoken language of its people. E.g., in English and Russian adjectives precede their nouns, in Spanish and Greek they follow them.

Considering that they've taught ASL to two other species of apes, it is rather surprising that more humans don't learn it. I can't believe there aren't times when it would be handy. Scuba diving, sitting on a turboprop commuter airliner, flirting with the chicas in the car in the next lane, band members trying to tell the roadies what they need, etc.

Oh, I didn't know that. I thought ASL was a language of its own, not based on another language's rules.

I see Moms at the park talking to their babys and toddlers in sign language more and more often.
http://www.signingbaby.com/main/

The sign language I know I think everyone can understand
it means different things depending on what fingers you use!

Actually, I think I'm wrong about that although it's not easy to figure out. According to Wikipedia American Sign Language was adapted from French Sign Language, and about 60% of the symbols are mutually comprehensible. (British Sign Language, on the other hand, was developed independently and is totally unintelligible to Americans.) I gather that French Sign Language was based on a sign language that was already in use within the deaf community in France. Since literacy was far from universal in earlier times, I can't figure out whether this sign language was based at all on the written language around them--and therefore is recognizably "French"--or if it was totally a priori.

So I retract my facile comment that sign languages emulate the spoken languages of their nation. I have no idea. I'll read more Wiki.

Sign Language is quite local. There are systems were you use your hand and mouth to make letters, which can be used in a broader context. More ordinary sign language, were signs are representative for words or concepts are more confined to different countries. Also you can have local dialects, meaning that you developed a local sign for some word. This would be incomprehensible for any out siders.

But apparently it's easier to learn another sign language than another spoken one. Perhaps ideas translate more naturally (and thus, consistently) into visual paths than into sequences of phonemes.

I guess so. My Girlfriend is a social education worker, and uses sign language every day at work. Its like written chinese. The piktograms can be read by anyone, because they are concepts more than written language. So even though they cant understand each others dialects, they can read the same paper anywhere. Anyone familiar with chinese can correct me of course, if I am wrong here :-)

Many of my friends taught their babies sign language. They were communicating effectively way before their 9-month birthday. It's pretty awesome to watch.

My college roommate did it with her daughter. It was amazing to me that the child had such a vocabulary and yet couldn't speak.

It's amazing to watch a baby do it. I was blown away. I think babies do try to communicate with us but they get frustrated and cry. The whole sign language with babies thing is fascinating.

There are also somewhat universal (at least in the dog training world) signs for commands you give dogs. Dogs are also excellent at non vebal commands; 90% of their communication IS non verbal anyway. All the verbal commands that my dogs know, they also know the hand gestures for the commands as well.
Like if I point to the floor, they assume the down position. If I hold my hand out in front of them palm up, they know that's the 'shake' or 'gimme your paw' command. Same for holding my hand up for a high five.