Does the Roman Catholic Church recognize marriages outside the church?

If a couple married in an Anglican Church and later divorced would one of them be able remarry in the RCC without getting an annulment (ie would the first marriage be considered valid)? What about other Protestant denominations? Civil marriages? Non-Christian marriages?

Different religions have different standards. You can always get a civil marriage without getting an annulment from your particular church since the state doesn't care about religion.

In Judaism, Orthodox Jews need to obtain a Jewish divorce before they can remarry. This is a document that is obtained by the husband to give to his wife, and it is the dissolution of the marriage in the eyes of Judaism; it essentially releases each party from the religious responsibilities of marriage. In the US, it's generally obtained after the civil divorce. One cannot be forced to obtain such a divorce since the rabbinical courts don't have civil authority.

I'm reasonably sure that Reform Judaism doesn't require a Jewish divorce, and not all Conservative rabbis require one.

In the Catholic Church, you have to have any previous marriages declared null before you can get married in the Church, whether or not they were marriages performed in the Catholic Church. Even if you're married in a civil ceremony, because the Church recognizes all marriages, as long as they're between a man and a woman. A declaration of nullity is just a fancy way of saying "annulment". The exception is is your spouse died, because that will end any marriage rather effectively.

Legal marriage in the eyes of the law is legal marriage.

I asked about this to a priest. I told him we were not married in the church (civil ceremony) although both were baptized though nonpracticing Catholics. He said we would have it annulled and then be remarried in the church to have the church recognize it. I asked him once annulled could I choose a different man? He said no. :(

Then why bother.

Once you are past the first marriage it gets trickier so trod carefully.