Sure. However, if you are concerned about the older friend passing away and the children or other heirs trying to get the car back (claiming that you unduly influenced the older person into giving the car to you for free) then it would be wise to at least have the older friend write out a statement or sign a statement that says the reason they are giving it to you is for all your help to her over the years. While not a guarantee, it as least gives you something to use if the heirs later claim they should get the car back. Perhaps an even better thing to do is to at least pay something for the car and have a receipt that says she is selling you the car for, say, $100 and that the low price is "because of all the help you have given me over the years" or something like that.
The Washington State Department of Licensing, usually located in the county administration building/complex is the location to transfer vehicle title by gift.