Ships can transfer cargo to exactly one foreign ship each turn. Historically, only the four minerals as well as colonists and supplies can be transferred this way, but there exist extended missions to transfer money and ammo as well. Since PHost 4.0h you can also use the transfer command to transfer money and ammo without affecting the ship's mission. If not all of the cargo fits on the receiving ship, you'll get it back into the normal cargo hold. If you do not have fuel, you cannot use the transporter, either. The Privateers can rob such transfers in transit. This does not apply to transfers between same-race ships. Those have no limit, and are performed instantly.
Ships can also unload cargo to a foreign or unowned planet. Likewise, only the four minerals, supplies and colonists can be transferred this way, but there is an extended mission to beam down credits, and an unload command. The Privateers can rob such transfers, too. Dropping colonists to an unowned planet colonizes the planet (you own it next turn), dropping colonists to an enemy planet triggers ground combat.
Ships in free space can jettison cargo. You can only jettison stuff when you have fuel. You can jettison minerals, supplies, and colonists. Some Winplan-compatible clients also let you throw away torpedoes, fighters and money.
Many of the starship missions interact with other ships, too. Ships can be repaired (and re-crewed) or recycled at starbases.