If you are looking for cheap flights without any preconceived ideas, you can try the solutions listed in Cheapest flight to anywhere at any given time or Travel site that found the lowest-price tickets from your current location
If you are looking for flights to several airports in the same area, many sites will let you include “nearby airports” in your search by checking a checkbox, including for example Skyscanner, Kayak, or ITA Matrix. See How can I do a "broad" search for flights? ITA Matrix even lets you specify a distance threshold and pick which nearby airports you want to include from a list. For an example, see Which is the cheapest way to get to Vietnam from Europe in summer?
Now, if you want to search an arbitrary list of airports and then choose between them by price (say want to go to either San Francisco or Tokyo), it's also possible on ITA Matrix and Kayak and maybe some other sites as well. It's not particularly user-friendly (or advertised at all, really) but it does work: Simply enter several airport three-letter codes separated by commas and set the other search options as usual (I am not sure how many you can put, three definitely works).
Note that broad searches are never guaranteed to find the absolute cheapest result because pricing all potential fare combinations is much more difficult than simply finding a route. Unfortunately, that's a common issue with flight search engines, see the discussions in What's a better way to find flights when cost is important and schedule is not? or Is there a flight search engine that combines flights from different airlines? or this presentation by Carl de Marcken from ITA [PDF].
This also means that broadening the search could actually produce poorer results. Obviously, the cheapest flights from narrower searches should still show up and removing constraints logically cannot exclude them but the search space quickly becomes too big for current search engines to handle.