Traveling spontaneously is one of the funnest things you can possibly imagine, but bar getting in your car and just driving wherever your whims take you, it is by and large much, much harder than it used to be.
You simply have to plan these days — but you can plan in such a way that all the spontaneity is not taken out of the trip.
When it comes to plane tickets and train tickets, if it is at all possible, try to travel during the off season, or at least during an off week. Stay away from major holidays, so that you can get a seat, as well as a good rate.
Beyond that, just ask the neighbors to take in the mail and you are good to go. Sure, you need to make plans for accommodations, but other than that, when you get to your destination, try not to plan your activities. Just go with the flow, you know?