Your question has 2 aspects to reply to:
- Physical limitations of the monitor itself
There are several display technologies. One of the oldest (and cheapest for a long time) is TN. It's prone to color shifts when viewed from different angles, esp. vertical. It is often used in laptops because it comes with good power characteristics.
Displays based on VA (MVA, PVA) and IPS (and some more exotic) are considered to be better suited for graphics/post processing. Critical colour shifts will be seen only at wider angles ... much wider angles.
If you are looking for differences (or a new monitor) you may visit http://www.prad.de
and take a look at their in-depth monitor reviews.
If you want to see how your monitor performs at different angles: http://www.lagom.nl/lcd-test/viewing_angle.php
There are some rules given by several institutes about workplace ergonomics for computer workplaces. As in most "soft" areas you will have a hard time to find hard evidence (well, "soft" is the opposite of hard, obviously) or reproducable data for their recommendations.
Using this as a disclaimer I suggest you google/bing/yahoo around a bit and look for something like "computer workplace ergonomics" or something like that.
One thing I have to suggest, because it cannot be said often enough: If you don't already own a *very good* chair, get the best one you can afford. If you haven't experienced the difference you won't believe what a good chair adds to your comfort/health and therefore to your productivity. Short term and long term. If you're young and laughing right now I understand. But just take a survey under the "old farts" and ask the desk jockeys among them and what their spine troubles are doing. Prepare for bleeding ears ...
PS: A viewing standard for eye-monitor-orientation is to have the upper monitor edge at eye level. Requires a vertically adjustable monitor stand which is not given for some "home entertainment" devices.