Do the Orthodox and Catholic Churches allow participation in each others' services? Is it alright for an Orthodox christian to go into a Catholic church and vice versa? That is:

Does either Eastern Orthodox or Catholic teaching object to occasional participation of an Eastern Orthodox Christian in a Catholic service (Mass)? What about occasional participation of a Catholic in an Eastern Orthodox service (Divine Liturgy)?
From a Catholic point of view, there is no problem with (a) a Roman Catholic attending an Orthodox Divine Liturgy and receiving communion or (b) an Orthodox attending a Roman Catholic mass and receiving communion. This is, however, restricted to circumstances when a Roman Catholic mass is unavailable.

The Orthodox position is different; Roman Catholics would not be permitted to receive communion in an Orthodox church and Orthodox would not be permitted to receive in a Roman Catholic church.

I've had surprising difficulty finding documentation for this, but here's an EWTN article explaining the Catholic position and here's an Orthodox Church of America page explaining the Orthodox position. They aren't exactly the best sources imaginable, but they are accurate in my experience.