Just wanted to add my experience. Did this last night on a car with 187K salty New England and Canadian miles.
Thanks everyone for all the advice!
Followed Rogue's procedure, but the car has stock intake manifold, so I had to move the power steering hoses and the charcoal canister out of the way.
So I had to do these additional steps before attempting to pull out the alternator (so, say, do these after you remove cruise control):
A. Detach the charcoal canister, two 10mm nuts attached to the firewall. Unscrew, then simply lift it off the bolts and swing it out of the way to rest on top of the intake manifold.
B. Remove 2 10mm bolts holding the bracket with two PS hoses in front of the strut tower. Lift that bracket off the bolts, so that you have room for the hoses to be pulled down.
C. Under the car, remove 3 10mm bolts (or loosen and rotate clamps out of the way) that hold down the PS hoses. I think all of these are attached to the PS rack itself. Two bolts are near each other, the third one is on *top* of the PS rack, towards the middle of the car. You can get it at it from the top or from the bottom, whatever's easier. Just follow the path of the PS hoses/lines.
D. Now you have wiggle room to push these hoses DOWN out of the way, which allows you to remove the alternator. Removing it is like playing tetris in your engine bay. I first got the pulley over the PS hoses and then was able to lift the alternator over the PS hoses. Then, I had to rotate it 90 degrees to lift it out entirely.
Tying rope over the alternator is very helpful. Getting it off the mounting point was a b****--it rotates, but doesn't want to come off. Lots of wedging with wrenches gets it moving. Keep working it.
Unfortunately, the long tension bolt attached to the P.S. pump broke and I can't start the car yet. Waiting on the part from the dealer.That's the last bit missing... everything else is back together.
So yeah, you can def remove your alternator without removing the intake manifold, the axle or the muffler.
Just for future searches, this is how I did it.
1. Disconnect the negative battery terminal.
2. Remove Cruise Control and bracket from strut tower (2 10mm nuts). Secure to or lay on windshield. I used a zip tie to attach it to the wiper.
3. Pop open the plastic cap and remove nut holding Terminal B Wire (12mm). Then pull on plastic housing to slide off. There are 2 clips on the back.
4. Remove Gray connector
5. Remove bolt that goes to the tensioner (12mm)
6. Loosen long tensioner bolt (12mm)
7. Remove the bracket that tensioner assembly attaches to (14mm). The bolt is behind the oil dipstick. I used a shallow socket with a 3" extension.
8. Go under the car and remove the long bolt that secures the Alternator to the bracket (14mm).
9. Rock Alternator back and forth while pulling up. I tied a rope around it to pull. This is the real hard part.
I didn't have to move any hoses to get the alternator out.