The fee for a license to use a sample can vary tremendously. The fee will depend on how much of the sample you intend to use (a quarter second is a minor use; five seconds, a major use), the music you intend to sample (a Madonna chorus will cost more than an obscure drum beat), and the intended use of the sample in your song (it is more costly to build your entire song around the sample than to give it only minor attention).
There are two different ways to pay for a license. First, you can pay a flat fee for the usage. A buy-out fee can range from $250 to $10,000 on a major label. Most fees fall between $1,000 and $2,000. The other way to pay for the license is a percentage of the mechanical royalty rate. The mechanical royalty rate is the amount a person pays to the copyright owner to make a mechanical reproduction (copy) of the song. A license which is a percentage of the mechanical royalty rate is generally between \ufffd \ufffd and 3\ufffd per record pressed.
I think these fees are the reason why sampling ala Vanilla Ice and the like is less common these days.