When I am using 24" displays, I put one in landscape directly in front of me and one in portrait off to one side. Upper/lower half of the portrait monitor works well for terminals / email / chat. Entire portrait for reading documentation. Full-screen landscape for everything else.

I find this works well for the "adjustable height desk" systems one puts on top of a regular desk. They usually aren't wide enough to have two monitors with one directly in front of the user. The portrait monitor, if the cables are long enough, stays on the fixed-height desk.

I'm unable to use two monitors side-by-side anymore. Working for hours with my head always turned to one side gives me headaches.

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Edited to add note on desk-placed "adjustable height" systems.