I have been looking for a way of finding out what over-the-counter stocks are being listed on reputable stock exchanges such as the NYSE.
Is there a website that keeps a list of those?
Check your broker's IPO list. Adding a new stock to a stock exchange is called "Initial Public Offering" (IPO), and most brokers have a list of upcoming IPO's in which their clients can participate.
Reuters has a service you can subscribe to that will give you lots of Financial information that is not readily available in common feeds. One of the things you can find is the listing/delist dates of stocks. There are tools to build custom reports. That would be a report you could write. You can probably get the data for free through their rss feeds and on their website, but the custom reports is a paid feature.
FWIW re-listing(listings that have been delisted but return to a status that they can be listed again) is pretty rare. And I can not think of too many(any actually) penny stocks that have grown to be listed on a major exchange.