OK, so just need to run an additional conductor for neutral and tie to the ground bar in the main panel. I wonder if this applies for my sub-panel in my outdoor garage as well. It has only 3 conductors coming from the main panel (2 hots and a ground/neutral). Would adding a ground rod in the earth, connected to the neutral/ground bar in the sub panel be required or rather an option? Or is my only option pulling another separate conductor all the way back to the main panel in the house (pretty much non-doable)?
Yes, additional (separate) conductor in the same raceway can tie to the neutral bus in the main panel. If this is the service panel, then the neutral bus will be bonded to ground with a giant green screw in the cabinet. EDIT: even when you have a brand new home built today, you should still separate grounds and neutrals in the service panel, and use the green screw to bond them together -- reason you want to do this is in case you add a whole-house generator later, as an automatic transfer switch usually becomes your bonded service panel, and then you have to re-route all those wires in your service panel to separate them. Better to keep them properly segregated to make life easier later.
For your outdoor shed: code changed in the 2005 cycle and again in the 2008 cycle. Prior to 2005, 3-wire feeds were permitted and neutral/ground could be bonded in detached building subpanels. 2005 allowed new detached buildings to use 3-wire feeds (bonded ground and neutral) ONLY if there are no additional metallic paths between the buildings (no cable TV wires, no telephone wires, no metal conduit). NEC 2008 eliminated this exemption and since its adoption, you must use a 4-wire feed for subpanels, regardless of conditions. Your building needs to conform to the code cycle in effect when the feeder was run (my 2008-built garage, for example, was built during the 2005 code cycle and uses a 3-wire feed, that's legal but I couldn't build it that way today).
All detached buildings or structures require a grounding electrode (or 2, see NEC 250.32 and 250.53(A)(2)). In many cases, it's already integrated with the concrete re-bar for a poured concrete floor, but sometimes you must drive a copper rod.
The reason for separation of grounds and neutrals is for safety reasons in case of a failure. I have a few posts on here that describes these failure scenarios (a garage with a broken neutral but bonded to ground and earth can return current through the earth or through an old, bonded appliance and create some really weird effects and/or shocks).
