Yes – In the UK, you can marry a cousin
This law was comissioned by Henry VIII who changed the law in order to marry his cousin!
However, there is medical evidence which shows that the potential risk of birth defects in a child born of first cousins was slightly higher than the risk associated with a non-cousin couple. Therefore it would be sensible to consult a GP to ensure that there are no genetic factors in your both parties health records that would make your decision to have children inadvisable on medical grounds.
Some countries have different laws concerning the marriage of cousins. I.e. some US states forbid it.
If you require more information you can contact you local Registrar. General for England and Wales, 01704-569824.