Gcol:
No, only oil based paints yellow with age. Most emulsion paints won't yellow with age at all.
And, not all oil based paints yellow as much as others.
You see, all animal fats and vegetable oils are "triglycerides" which means that the fat or oil molecule consists of three hydrocarbon chains called "fatty acids" connected to a glycerine molecule. Different kinds of vegetable oils contain different kinds of fatty acids, and it's the kind of fatty acids there are in the oil that determine how much a coating made from that oil will yellow with age. The most common drying oils used in coatings are Safflower Oil, Tung Oil and Linseed Oil. Of those three, Linseed Oil contains the most of a fatty acid called "linolenic" fatty acids, and linolenic fatty acids produce the most yellowing. As a result, paints and varnishes made from linseed oil yellow more than varnishes made from Tung oil (which contains very few linolenic fatty acids).
Similarily, alkyd resins are made by modifying soy bean oil which wouldn't dry to a film naturally the way linseed oil does. Soy bean oil contains mostly linoleic fatty acids, and they don't cause as much yellowing as the linolenic fatty acids in linseed oil, so alkyd paints yellow less than boiled linseed oil based paints.
Go to this web site:
http://www.seatons-uk.co.uk/home.aspx?d=content&s=62&r=109&p=451#
and click on the link "View typical fatty acid profiles" to see average values for the kinds of fatty acids found in each of the most commonly used oils for making paints and coatings out of.
Linolenic fatty acids are the worst for yellowing, and linseed oil contains the highest amount of those kinds of fatty acids, so linseed oil based paints and varnishes yellow more than other kinds of "oil based" coatings.
But, although it's not common knowledge, the yellowing in oil based coatings is reversible. If you expose the yellowed paint to direct or indirect light from the Sun, that yellowing disappears.
Take a look at this web page:
http://aic.stanford.edu/jaic/articles/jaic24-02-002.html
The yellowing of oil based paints used by artists over the centuries is a problem for museum curators who generally have more oil based paintings in their collection than they can display at any one time. Consequently, many old oil based paintings have to remain stored in boxes for years before they are put on display. But, storing old oil based paint under dim lighting conditions causes the oil based paint to yellow.
The above study showed that the centuries old practice of taking oil based portraits outdoors and exposing them to sunlight is effective in eliminating the yellowing that occurs in oil based paints under dim lighting conditions. And, that elimination of the yellowing by exposure to sunlight can be performed over and over again.
So, if you have any yellowed oil based paint in your house, you can eliminate the yellow from it by positioning a bloody great mirror to reflect sunlight onto that paint. (And, in fact, even indirect sunlight is effective in eliminating the yellowing that occurs in oil based paints with age.)
Anyhow, Gcol, now you know why some oil based coatings yellow more than others, and that you can eliminate that yellowing by exposing the paint to sunlight. But, the sad state of affairs is that by reading these last few paragraphs, you now know more than most people working in paint stores about yellowing in paints and what can be done about it. And, as I've said in previous posts, there's no good reason for that since none of this stuff is complicated or difficult to learn. The real problem is that there's no one teaching it.