In the US

SPG->AA
Starwood transfers to AA and other airlines. 1:1 with minimums depending on your Starwood status, if you transfer 20,000 Starpoints, you get 25,000 miles. There are maximums. The points+the bonus need to be under the cap, and transfers are not instant.

AX MR -> SPG -> AA
American Express MR transfers to Starwood, but at a rate that is viewed as unfavorable to most. You can transfer 1000 MR to create 333 Starpoints. Sometimes there may be an offer that increases the number from 1000:333 to 1000:500.

SPG->US->AA
Same rates/rules as SPG->AA, but you have to wait a year or so for the merger before the US points will [probably] become AA. The only reason why this might be considered is if it works around a transfer limit.

Except for AMEX MR, you can't transfer in Starpoints. You can purchase Starpoints for $35/1000, occasionally $28/1000. It would probably be cheaper to buy the AA miles directly than via Starpoints.

Excluding Starwood stays, the AMEX SPG card is the other way to earn Starpoints.