To cherish means 'to adore' or to appreciate (to give great value to someone or something). "I cherish our friendship / my children / the gift you gave me" How commonly used "I cherish you" is, depends on how frequently you directly express that feeling to someone. It sounds very solemn and you'll hear it a lot in wedding vows.

@David and Honey, Thanks

to love, protect, and care for someone or something that is important to you Although I cherish my children, I do allow them their independence.

It has a similar meaning. Although it is not nearly as common as saying "I love you", it is regularly used and a phrase everybody understands. There was a popular love song from 1996 called "Cherish": https://www.youtube.com/watch?v=nJztW9dcpyc