Is the Nikon SB 400 compatible with?

The Nikon D3000 and Nikon D3200?

Yes it is, but it has no remote capability.

It is compatible, and it should work well. However, it can be worthwhile to spring for the more expensive SB700. That has more power and adjustability. For using bounce flash that can be very useful.
If you get an SB400 and later want an SB700, the SB400 is not necessarily wasted. It could provide service in a multiple flash setup.

Yes, but I wouldn't waste money on the SB 400. I'd go for the SB 700.

http://www.amazon.com/...0042X9L6A/

(You might have to add the item to your cart to see if there's a difference between the listed price and the actual prize you'll be paying. You can always remove the item later.)

SB 400 is compatible with all nikon dx cameras. It is handy and small and price is great. If you want more power you can go with sb 700 or 800 or 900 with a higher price tag…