Texture resolution

[Branan]

Most graphics hardware from the past 7 years or so will have a limit of 4096x4096.

Most displays from the past 7 years have less than 2048 pixels in any direction. Most times a texture will have less than 1024 pixels visible. Higher res doesn't help if there aren't enough pixels on the monitor to show it off

[tachzusamm]

True, but only if:
a) The textured object fits into the current view OR at least part of the object containing one texture tile fits on the screen (e.g. for repeated patterns)
b) The texture is viewed orthogonally

Higher res DOES help when you view only a section of the texture, e.g. when you stand close to a large rock, look down to your feet standing on a ground plane or watch the sky (chances that you can view a whole sky dome on your screen are very low).
In these cases the visible part gets kinda zoomed in (scaled up), and you WILL recognize if it's low-res or high-res with details.