I assume you mean by pure battery power.
Long-distance heavy goods vehicles: probably not although companies like Scania are developing them.
Ironically, small (up to about 3t) battery-electric wagons were common in many European and American cities in the 1890s-1900s, mainly used to shuttle freight between railway goods-yards and local businesses.
Among them were many battery-electric, private cars, too; and those were allowed on the roads in London's Royal Parks from which these new-fangled, noisy, smelly, petroleum-spirit fueled equivalents were barred!
Trains. Yes, at least for passenger-trains. It takes far less power to accelerate a given load from rest to a set speed, and maintain that speed, on rails than on roads; and experiments with battery-electric traction are under way.
The world's first public-carrying trials of such started recently on a short line in the London suburbs.
Since Diesel multiple-unit trains with the engines under the coach floors are already commonplace, I see no reason against battery-electric equivalents replacing the DMU for inter-city and suburban routes.
Whether a BEMU carrying, say, 200 passengers would manage the Nullarbor Straight on a single charge, at night with the coach lights and heaters on, remains to be seen! (Steam locomotives had to stop for water part-way, so why not a recharging stop?)
Aircraft: There are already experiments, mainly in Sweden I think, on electrically-powered aeroplanes of limited capacity for short flights. No-one proposes such for intercontinental flight; but the real question there is need for so many flights in the first place.
Ships: Not batteries but fuel-cells perhaps. A large ship requires enormous power to push it through the water, and so far, using batteries for vessels is limited to slow-moving leisure and tourist craft on inland waterways.
