Can a Catholic marry someone who is not Catholic?

Roman Catholic Answer

from The Catechism of the Catholic Church, second edition, English translation 1994

1633 In many countries the situation of a mixed marriage (marriage between a Catholic and a baptized non-Catholic) often arises. It requires particular attention on the part of couples and their pastors. A Case of marriage with disparity of cult (between a Catholic and a non-baptized person) requires even greater circumspection.

1634 Difference of confession between the spouses does not constitute an insurmountable obstacle for marriage, when they succeed in placing in common what they have received from their respective communities, and learn from each other the way in which each lives in fidelity to Christ. But the difficulties of mixed marriages must not be underestimated. They arise from the fact that the separation of Christians has not yet been overcome. The spouses risk experiencing the tragedy of Christian disunity even in the heart of their own home. Disparity of cult can further aggravate these difficulties. Differences about faith and the very notion of marriage, but also different religious mentalities, can become sources of tension in marriage, especially as regards the education of children. The temptation to religious indifference can then arise.

1635 According to the law in force in the Latin Church, a mixed marriage needs for liceity the express permission of ecclesiastical authority. (Cf. CIC, can. 1124) In case of disparity of cult an express dispensation from this impediment is required for the validity of the marriage. (Cf. CIC, can. 1086.) This permission or dispensation presupposes that both parties know and do not exclude essentials ends and properties of marriage; and furthermore that the Catholic party confirms the obligations, which have been made known to the non-Catholic party, of preserving his or her own faith and ensuring the baptism and education of the children in the Catholic Church. (Cf. CIC, can 1125)

Note: In other words, you need to speak with your pastor right away, if he approves of the marriage, he will seek the appropriate dispensations from the Bishop.
 

Answer

Yes, of course they can as long as they get married in a Catholic church and the children are Catholic...
Nota Bene: The above is presuming that the non-Catholic party is at least baptized and that a dispensation has been secured from the Catholic Church for the Catholic party in order that the marriage can go forward.