The Unihan standard contains a field for many of the characters that classify frequency. This data and other data gets aggregated from scholarly sources which the standard discloses in its notes. Note, Unihan will also contain the Korean and Japanese variants in use.

See: http://www.unicode.org/charts/unihan.html

and

http://www.unicode.org/reports/tr38/#AlphabeticalListing and search for field, kFrequency.

I have prepared Unihan 5.1.0 into a sqlite database a couple years ago, here: http://guwen.hiddenstorehouse.com/

The current version is Unihan 6.0 and I have not processed it.

The Unihan standard contains the kFrequency field. This fields gives you a general idea of how frequent the character shows up. This data and other data gets aggregated from scholarly sources which the standard discloses in its notes. Note, Unihan will also contain the Korean and Japanese variants in use. As far as I know, it does not have data for character combinations. Some of the other answers point to resources that does have that data.

See: http://www.unicode.org/charts/unihan.html

and

http://www.unicode.org/reports/tr38/#AlphabeticalListing and search for field, kFrequency.

I have prepared Unihan 5.1.0 into a sqlite database a couple years ago, here: http://guwen.hiddenstorehouse.com/

The current version is Unihan 6.0 and I have not processed it.