In Virginia, it is a crime to record any "wire, oral, or electronic communication" unless one party to the communication consents. Virginia Code § 19.2-62. This means that you have to be involved in the communication directly in order to be able to record, and even then you have to be careful or you might run afoul of the law. Different states have different laws for recording communications, and if one person is in Washington D.C., or some other state, different laws may apply.
The Virginia law covers oral communications when the speakers have an "expectation that such communication is not subject to interception under circumstances justifying such expectations" Virginia Code §19.2-61. This means that the speaker needs to have an expectation of privacy. Conversations made in public spaces may not have this protection; the privacy determination is heavily dependent on the surrounding circumstances of the spoken communication.
A person who "[i]ntentionally intercepts, endeavors to intercept [...] any wire, electronic or oral communication" may be found guilty of a Class 6 Felony. Class 6 Felonies are punishable by fines and imprisonment. Virginia Code § 18.2-10(f).
There is also a civil remedy for the unlawful interception of a communication, which includes actual damages, punitive damages, and attorney's fees and costs. Virginia Code § 19.2-69.
If you believe that someone is listening in on your private conversations, you should contact an attorney. Similarly, before you begin recording conversations, you should speak with an attorney.