I disagree, there are tests such as this:
http://www.eskimo.com/~miyaguch/power.html
which have no time limit, yet are very difficult. I don't think "everyone" has the ability to answer all of these questions.
"Without the time constraint, an IQ test wouldn't really measure anything at all."
It may measure how well you are able to abstract problems.
Whether or not it has much to do with your ability in different disciplines is another matter, but arguing that it is simply down to timing seems somewhat silly.
Given a finite amount of patience (or, equivalently, a time-constraint, which sets "patience" to a known quantity instead of allowing it to vary per individual), we can give a person an infinite stream of unit-sized lateral-thinking problems, and then see how many will be solved correctly before they "hit the wall." This is then a measure of their ability, in general, to recognize patterns quickly enough to put these insights to use: IQ.
Everyone can recognize a pattern or get a lateral thinking puzzle eventually. Adding the time-constraint splits the world into people who can recognize patterns quickly enough to employ that pattern-recognition in the course of their every-day life, and those who can't: thus, IQ. Without the time constraint, an IQ test wouldn't really measure anything at all.
IQ is believed to relate to intelligence because the ability to see patterns sufficiently quickly gives you a kind of "intuition" for new subjects. It's like a lubrication against friction: without it, new subjects will be "at rest" in your mind, and you'll have to give them a push to get your understanding of them going. With it, they'll just slide down the funnel right into your brain. :)
More technically, IQ could be seen as a measure for how much of a cost your brain puts to engaging your type-2 reasoning (http://lesswrong.com/lw/531/how_you_make_judgments_the_eleph...). As expected, glucose, butter, CNS stimulants, and other things that make the brain think it has more "stored resource" to work with, are measured to enhance IQ--because they lower the brain's calculation of this cost, and therefore allow you to engage your lateral-thinking processes more easily and more often. Likewise, hunger, depression, and other things which raise your brain's cost evaluations unilaterally, also raise the cost of engaging your type-2 reasoning, and thus lower your IQ.