The main hindrance to a widespread market penetration of battery-powered electric vehicles (BEVs) has been their limited energy reservoir resulting in cruising ranges of few hundred kilometers unless one allows for recharging or switching of depleted batteries during a trip. Unfortunately, recharging typically takes several hours and battery switch stations providing fully recharged batteries are still quite rare – certainly not as widespread as ordinary gas stations. For not getting stranded with an empty battery, going on a BEV trip requires some planning ahead taking into account energy characteristics of the BEV as well as available battery switch stations. In this paper we consider very basic, yet fundamental problems for E-Mobility: Can I get from A to B and back with my BEV without recharging in between? Can I get from A to B when allowed to recharge? How can I minimize the number of battery switches when going from A to B? We provide efficient and mathematically sound algorithms for these problems that allow for the energy-aware planning of trips.