A fallen tree blocked Larch Road near Limavady in Co Derry
Hundreds of households, particularly in counties Derry and Armagh, lost power but most were restored quickly.
It was the first of two storms to hit the UK and Ireland this week, with Storm Eunice expected on Friday.
Warnings have been issued by the Met Office, with northern England and Scotland the worst affected in the UK.
On Thursday morning, Northern Ireland Electricity (NIE) reported no major faults across the power supply network.
A yellow warning was in force in Northern Ireland from 13:00 GMT until 06:00 on Thursday.
An amber warning, the second highest level of warning, was also issued for northern parts of counties Derry and Antrim from 2 pm until 11.59 pm on Wednesday.
The Met Office warned of the potential for wind gusts inland of about 100km/h (60mph), with stronger gales along some exposed coasts and hills.
It said injuries and danger to life were likely from large waves and beach material being thrown on to roads and sea fronts.
The disruption caused by Storm Dudley included:
At one point, more than 800 homes were without power across Counties Derry and Armagh
More than 100 people were still without power in the Armagh City area at midnight
Traffic on the Foyle Bridge restricted to 30mph due to strong winds.
A number of roads were blocked or partially blocked by fallen trees including:
Mobouy Road in Derry
Larch Road near Limavady.
In the Republic, Met Éireann issued a yellow warning across the country for westerly winds associated with Storm Dudley.
The Irish meteorological service warned of winds reaching mean speeds of 30-40mph with damaging gusts of 50-65mph, which will be stronger on exposed coasts and on high ground.
Storm Dudley will ease on Thursday to leave a brief calmer spell before Storm Eunice arrives on Friday.
For Storm Eunice, yellow warnings are in place for winds and snow affecting Northern Ireland, southern Scotland and northern England.
The warning comes into force from 3 am on Friday and runs to 6 pm on Friday.
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