Can all Nikon flashes work on different Nikon dslr cameras?

I'm about to buy a speed flash for my Nikon D3000, but I really don't know about flashes. The Speed light is called SB-16 Speedlight. Would that work on mine?

Don't. What you really need to do is go to a store with your camera and match the connections between flash and camera or… If you're on line, read the specs to learn what cameras that flash is designed to fit.

That is an oldie.
http://www.mir.com.my/rb/photography/hardwares/classics/nikonf3ver2/flash/sb16ab/manual/index.htm
If the unit has the ISO coupler it should work, although you may have to use manual settings on the camera.
With older flashes designed for film cameras, trigger voltage may or may not be bad for the electronics of a digital SLR.
According to
http://www.botzilla.com/photo/strobeVolts.html
the SB-16 should be safe.
I think you would be happier with a new SB 700.

Yes it can but will work in manual mode.
NO AUTO, NO i-TTL, nothing only just fire flash