Most of the time when I first turn on the A/C in our 2008 Toyota Sienna, the air that blows out has a very distinct chemical - nasty smell. After a while it seems to go away. I'm not sure if I just get used to the smell or it actually goes away. When I just turn on the fan with no A/C there is no smell. Also if I drive somewhere then leave shortly thereafter, it doesn't stink when I fire it up the 2nd (or subsequent) time. Should I be concerned for my health or safety?
This is a common problem for all air conditioners (in a car or not), and is caused by mildew growth. In cars it often happens when people run their A/C on the recirculation all of the time, or the drain gets clogged. The system doesn't dry out completely and mildew starts to grow.
You should be concerned about your health, especially if you have allergies. Just imagine all that mildew and god knows what else growing in there and being spewed in your face every time you turn the A/C on... Here's a link to US EPA page describing how mold may affect health, if you are still not convinced.
The things you should do to remove the cause of your problem and prevent it from happening again:
Run it on recirculation only when something stinks outside, or you want it to cool down quickly. Fresh air from outside will help it dry out better.
Make sure that your A/C drain isn't clogged and there is no water building up.
And this is what you could do to remove the unpleasant effects:
Run the heater on full for a while, that will dry out the system and might 'cook' the mildew.
Change your cabin air filter (if you have one).
There are special sprays sold to remove the mildew from the A/C system (read the instructions carefully before using them). Just using Lysol or some other stuff like that will work too, but the smell will be more unpleasant.
I suggest that you do all of this, and in the specified order.
I have observed this - kind of like an acrid or "vinegar" smell.
You can help prevent this by turning OFF the air conditioner a couple/few minutes prior to turning off the auto.
As others said, it is caused by growth of biological bacteria/fungal and turning off early helps dry the system and assists in prevention as it reduces the moisture retained in the system.
First, it's fungus that's growing in all a/c. You can remove it yourself by using an anti-fungal spray at a fitment centre. Spray it on the outside where the wind gets into the car. When you turn your interior fan on there's a suction entery place where the air goes enters your engine bay, spray it there. It will get sucked into the pipes straight to where the fungus is.