How much tea is ideal out of one tea bag?

This completely depends on the quality of the tea and flavor you're going for. It is common practice (especially in China) to make 2-3 or more cups/pots of tea from good quality loose leaf green tea. The flavor will change after each steeping, becoming lighter and milder, but also just different in certain ways. You can do the same thing with any lower quality tea, you just have to decide if you like the flavor of the second, third, etc. steepings. If not, don't do it.

After looking into this much longer than a sane person should have, I've realized that the strength of the tea doesn't depend so much on the quantity of tea. Controlling the strength of tea is normally done by controlling the steeping time. As stated by paul, the best way to dilute the strength of a tea is by resteeping it.

The steeping time of a tea is most determined by the coarseness of the tea leaves. Similar to garlic, finer leaves make the taste a lot stronger, whereas large, coarse leaves will be weaker. The instructions on the bag often say what's been tried and tested.

Quite often, one tea bag can make quite a lot of tea, enough for a teapot. I'd recommend going for two tea bags only if you're planning to go for larger than a teapot, for tea suited to drinking by itself and with added ice, or with certain weaker teas.

For black tea, the common steeping seems to be 2-3 minutes. There's little harm in steeping too short, but steeping too long will create a harsh bitter taste (though some people may actually want that). For cheap, harsh, unbranded teas, 3 minutes seems to be enough unless the leaves are finely chopped.

Don't shake the tea bag or stir the drink while steeping it, because it will cause the harsh stuff to enter water faster, and black tea should be steeped at 98 degrees C.

Your tea bag will contain what the manufacturers deem to be the right amount of tea for their customer.

So if you buy a cheap brand, low quality tea you will not be expected to make the same amount of effort as you will never get a quality cup of tea from it, 1 bag [to] 1 mug, boiling water, stir squeeze and drink.

Not in my opinion an ideal cuppa. If you want a proper cup of tea you need to steep (brew) your tea for 3.5 mins and don't squeeze the bag as this releases bitterness into your brew. The tea bag will contain 2-3 grams of tea. And never, never reuse an old tea bag.

One cup per bag is a good rule of thumb. Depending on your tastes as well as the type and quality of the tea, you could make 1-2 cups per teabag. Avoid steeping too long or else the tea will become bitter, particularly for black teas.

Personally I'd say 1 tea bag per mug, however in slightly larger mugs leaving the tea bag in a wee bit longer should also be fine (not too weak).

most teabags will have instructions printed on the packaging, indicating what quantity of water they were intended for and how long to steep them.
With single-cup bags becoming ever more popular (handy for the office, not so much for at home IMO) you just have to be careful which bags to buy :)