Yes, you are able to park for free, and you can use any Disney transportation (buses, boats, monorails), whether you're staying on site or not. You may be asked to show a photo ID at the guard shack upon entering the parking lot.
At certain very busy times of year (Christmas, other holidays), parking may be restricted at certain resorts, typically the deluxes closest to the theme parks. If you happen to be visiting at one of those times of year, you might need a reservation at one of the resort's restaurants to park there. Or, you can combine your resort visit with a theme park visit, and just leave your car in the theme park lot and take Disney transportation to the resorts.
For instance, the MK parking lot (TTC) has monorail access, and from there, you can visit all of the monorail resorts. If you're in Epcot, you can exit through the International Gateway between the UK and France, and walk or take a boat to YC, BC, the Boardwalk, Swan, and Dolphin.