Catholic and Authodox churches still have quite a few fast days. Some are supposed to be complete fasts (Ash Wednesday, Good Friday, Christmas Eve) and some are partial. Most peopl just exclude meat/poultry for the fasts or fast from midnight, if at all. Its covered in the easter/goodfriday thread that I linked above.

Disclaimer: Not after a debate on the pros or cons of circumcision. Also Yael (and any other Jewish readers) I'm just putting down some historical facts, I don't personally follow the belief that my religion is right and someone else's wrong and ergo they are going to hell/eternal damnation.. for me that's not what my religion is about... I don't follow my religion for what might happen after I die but for now and who I am while I am living. For me being Catholic makes me a better person, and I whole heartedly support any religion that does just that, makes someone a better person and a better member of society, regardless of what that particular religion is.

Catholics, like Jews, have a list of laws we are supposed to follow on how to practise our religion, it is called the Catechism. It deals with the dogma of the religion, the laws, practices and feasts.

In regards to laws of the old testament and those of the new (as they pertain to catholics) :
From the document, "Cantate Domino" (A.D. 1442), signed by Pope Eugene IV, from the 11th session of the Council of Florence (A.D. 1439, a continuation of the Council of Basle, A.D. 1431, and the Council of Ferrara, A.D. 1438) :

[The Holy Roman Church] firmly believes, professes and teaches that the legal prescriptions of the Old Testament or the Mosaic law, which are divided into ceremonies, holy sacrifices and sacraments, because they were instituted to signify something in the future, although they were adequate for the divine cult of that age, once our Lord Jesus Christ who was signified by them had come, came to an end and the sacraments of the new Testament had their beginning. Whoever, after the Passion, places his hope in the legal prescriptions and submits himself to them as necessary for salvation and as if faith in Christ without them could not save, sins mortally. It does not deny that from Christ's passion until the promulgation of the Gospel they could have been retained, provided they were in no way believed to be necessary for salvation. But it asserts that after the promulgation of the gospel they cannot be observed without loss of eternal salvation. Therefore it denounces all who after that time observe circumcision, the [Jewish] sabbath and other legal prescriptions as strangers to the faith of Christ and unable to share in eternal salvation, unless they recoil at some time from these errors.
In “Nineteen Letters,” Rabbi Hirsch said that God is the “Harmonizer of Opposites.” He did not saythat God is the “Segregator” of opposites. I've often wondered over this, weather it was to do with the issue of equality of the sexes and that God viewed both men and women worthy of all official religious ranks or if it was more to do with Harmony amongst religions. I mean I feel that essentially the monodiety religions (Judaism, christianity, Islam) have the same fundamental beliefs BUT that they differ in their interpretation on practices... why then can't we be harmonious with the same god. I have always taken this to mean we aren't supposed to be fighting or arguing over religion.