If I'm not mistaken a Roman Catholic can receive Communion at an Orthodox Church. But as far as I know the Orthodox members do not receive Communion and a Roman Rite Church.
The issue is the validity of the sacrament.
Catholics and Orthodox don't have intercommunion one with another because of our disagreements in the past. It is a matter of discipline that can, and has, been waived in certain circumstances. But we believe that each other's sacraments are valid.
(For example, I believe the official position of the Church is that we may receive communion, if the Orthodox priest is willing to distribute it to us, if there is not a Catholic church within a reasonable distance)
However, with the other Western ecclesiastical communitites, we do not believe that their communion is a valid sacrament. There is no transubstantiation in any of their rites. This is because we do not believe that there is a valid apostolic succession and, thus, no valid sacrament of Holy Orders. Reception of bread and wine/juice in any of the worship services of those communities would be a public scandal, as it would indicate that we accept the validity of their ceremonies.
As to the beliefs of the schismatic western communities (protestants), I believe that Anglicans think there is transubstantiation, while the Lutherans believe in something called "consubstantiation" -- that the body and blood are 'spiritually' there, in addition to the physical presence of the bread and wine. I also think that the Lutherans believe that the spiritual presence of Christ leaves immediately when the service is over. I believe that the other groups simply consider it to be a symbolic thing...they are doing it to recreate the last supper.
(Having said that, I'm no expert on the theologies of various protestant groups, so if somebody wants to correct me about my statements on them, I'll accept the correction gladly)