Is there a website or tool to see how many people are searching for certain terms or groups of terms on the major internet search engines?

Google: Adwords Keyword Tool

I have no idea never really thought about it.

Adwords Keyword Tool will tell you how many searches are being performed on Google (Yahoo and MSN both have comparable tools as well), but if you are interested in searches across all search engines you can use WordTracker Free or SEObook Keyword Tool.

There are other tools and services that will yield more accurate results, but the will cost money to use.

Google Trends is great. You can even compare multiple search terms at once.

@Eambos The only problem with Google Trends is that it gives you a visual graph representing volume which is great for showing how media and seasonality affect search, but it doesn’t actually show how many searches make up that volume. Basically the value of 1 in the Google Trends graphs holds a different value for each term you search so be sure to read the data as a trend instead of a value.