The only current reciprocal privileges I know of are with Qantas- clubroom access for AC members when flying Qantas.

There were reciprocal privileges with USairways which ended around when they ended the frequent flyer partnership with AA in 2001; used to be possible to combine miles from one person's AA and US ff accounts to redeem an award in either program.

There were also agreements allowing AC members to use Ambassador Clubs before TWA was integrated into AA and with Canadian Airlines to use their lounges when flying them until they were merged into Air Canada.