Most games are using 24 bit textures now, or are at least providing the option to use them and in some cases include an 8bit alpha channel aswell. Combined with high resolutions (screen and texture) and a reliance on texture memory for various lighting and shading techniques you can quickly run into problems though.
I would say create all your textures in 24bit and if you run into problems just convert them to a lower bitdepth when you load them. Also try to batch surfaces together when rendering to minimise texture swapping.
In some situations you can get away with low resolution, low bitdepth textures and you should make sure you take any chances to do so as it will free up memory for prettier textures elsewhere and speed up rendering too.
I wouldn’t ever recommend cutting the framebuffer colourdepth though as this is where you’ll be compositing the final image (especially when dealing with blending/multipass rendering).