Here's a label from a Neem product: http://www.montereylawngarden.com/pdf/70NeemOil-Label.pdf
Seems like the mix is 1/8th cup Neem oil, 1 tablespoon of dish soap (I use Dawn because that's what we buy) and a gallon of water. Kills aphids instantly (well, any oil should since it just covers their air holes and drowns them), helps with black spot, kills spider mites, gets rid of grasshoppers for a couple of days when they get bad. The soap acts as an emulsifier so the oil will mix in the water. I got a little 40 oz hand pump sprayer at Wal-Mart and mix one tablespoon Neem, one teaspoon Dawn, 36 oz water, shake and spray. I wish I had gone with a bigger sprayer because I have to mix two bottles to get all my plants -- tops of leaves, bottoms of leaves, stems and the top of their soil.
I get itchy dry hands, knees and neck working outside in the summer and a couple of drops of Neem oil in a little trial bottle of hand lotion makes the itching stop immediately. Even just mixing it in a little spray bottle with water and spraying my clothes helps keep mosquitos away without putting DEET on my skin...although it doesn't last as long so when we go camping I still use OFF :>)
If you want, I have a few more links in my bookmarks somewhere that I can find. I bought my bottle at Gardens of the Ancients near 290 and the Flea Market in Austin. I assume that guy still reads the newsgroup? After a year mine got thick and doesn't seem to work as well so I'd suggest getting the 8 oz bottle more often than having a bottle go bad on you. I think it was $25 for 16 oz which sounds like a lot but it has lasted me well over a year now...
Found Neem oil one time when I was trying to kill black spot and aphids with the same organic spray because I was lazy...been happy with it for awhile now.
John now in Houston