0,0 in UV space maps to the lower left corner of the lower left texel, assuming you're loading a lower scanline first bitmap (it's the upper left corner of the upper left texel if you're loading an upper scanline first bitmap manually without conversion).
The center of the lower-left texel is at 0.5/Wt, 0.5/Ht, where Wt is texture width, and Ht is texture height, for the texture MIP level that you're sampling from. This means that different MIP levels need different amounts of bias to find the center of a texel.
0,0 in homogenous screen space maps to the center of the centermost pixel in Direct3D9. When the width of the render target is even, I don't know which particular pixel it chooses.A corner of a pixel, which should coincide with a U/V of 0,0, is at a multiple of N where X,Y is (2N+1)/Ws,(2N+1)/Hs, where Ws is width of screen in pixels, and Hs is height of screen in pixels. Note that, because of the "0,0 is a pixel center" rule, you don't hit 1.0 perfectly at the edges of the homogenous space. Here, I think OpenGL is better, in that it maps 0,0 to the intersection betwen the four center pixels, so it's analogous to texturing.
The fact that 0,0 is in the center of a pixel comes from how the viewport transform goes after the projective divide, and the requirement that pixel centers are at integer coordinates (in viewport coordinates). Unfortunately, there is no "Direct3D Specification" similar to the OpenGL specification, so you have to figure this out the hard way, by reading the available documentation and drawing conclusions.
Finally, rasterization of a pixel happens when the center of that pixel falls within the rasterized triangle, or exactly on the upper or leftmost edges of that triangle. I believe that a "topmost" edge that slants dowards to the right does not count as "upper", because the dual edge on a connecting triangle would count that as "leftmost" -- but, again, there's no firm spec accessible to people without the REF source code.
I have found these rules to largely be followed by modern drivers for modern hardware. The main exception are some ATI graphics cards, which have a control panel option for "alternate texel center," which would screw up these rules when enabled. By default, this checkbox is not enabled, and the rasterization follows these above rules.
In general, to map a one texel texture to one pixel, you want to plug U/V of 0,0 through 1,1 into the quad texture coordinates, and plug screen coordinates of -1/Ws,-1/Hs and 1/Ws,1/Hs into the quad position coordinates.
I hope this helps, and if I've drawn an erroneous conclusion somewhere, I'd like to be informed of it. However, following the above rules in Direct3D has always given me 1:1 texel/pixel alignment, so I'm of the belief that the above is correct.