If I am a US citizen and my boyfriend has a visa, can we cross into the US together without a problem?

Significantly more information is needed in order to provide a legal analysis. Of course, you, as a U.S. citizen, may enter the U.S. by showing your U.S. passport. In general, a foreign national may use his valid visa and his passport to enter the U.S., but some exceptions apply, such as if the foreign national has a visitor's visa (or some other types of nonimmigrant visas) and his intention is to become married and apply to remain in the U.S. as a Permanent Resident. If that may be his intention, then it would be wise for you and him to consult with an immigration attorney who, upon learning all of the relevant facts, could advise about eligibilities, options, and strategies to attain your goals.