There are some HYIP sites where you "invest" a certain amount of money, it accrues interest daily, and at the end of a set term, you can withdraw your earnings. I have tried this on occasion, but usually they are just scams. Essentially they are little more than a ponzie scheme. The way they make money is to get others to invest in their program. As long as people continue to invest in it, they can pay the earnings to the people that had invested earlier. Which means if you get into it early enough, there is a chance that you can earn a high interest on your money in a short period of time. However as soon as the site cannot get any more investors (or at least enough to pay the earning to their current investors), the scheme collapses and any money you had invested are lost. If this is what you were thinking of, then I'd warn you to be cautious and only use money that you don't need; treat it like you would going to a casino... you might hit it just right and double your money in a few months, or the site might collapse and you lose it all.
Gomez Peer Zone is another site to look at. They actually use your internet bandwidth to run different projects and then pay you based on how much time your computer is online as well as how much "processing" time (the time when they were actively using your bandwidth). It runs in the background and only uses the bandwidth that you are not using. So if you are downloading a large file, then this will stay idle whereas if you are just reading a web-page and are not click through various links, then it had a chance to use your bandwidth. You don't get paid a whole lot but considering you don't have to do anything active in order to make money, it is about as close to "making money while waiting" as you can get. And unlike the assorted HYIP sites, this is pretty legit; I've even seen news reports that use Gomez for their statistics, so you know that the statistics they are gathering actually have a use in the market place.
Other than that, I'd just suggest a normal investment medium (eg stocks, bonds, mutual funds, etc.) if you just want to invest some money and wait it out to receive earnings. They may not be able to pay such a high rate of return, but at least you know there are stiff regulations to keep everything legit.