Problems at the airport began on Saturday at 6am when the luggage sorting system broke down, spokesman Bertrand Stämpfli is quoted as saying by the ATS news agency.
Baggage had to be sorted by hand and extra staff were called in to deal with the backlog.
But the holdups led to some planes leaving without luggage, ATS reported.
A breakdown in communication between the European baggage management system in Norway and the Geneva airport was fixed by midday.
But delays continued through the day, exacerbated by other technical failures, including a breakdown of the instrument landing system because of ice at around 1pm.
At the same time, snow caused visibility problems and 22 flights were rerouted to destinations such as Basel, Zurich and Turin, Italy.
The ILS was fixed in 50 minutes but 35 flights were cancelled and delays of up to five hours were recorded.
Meantime the airport had to cope with a fire in one of its escalators and another one in a restaurant, ATS said.
The airport authorized flights an hour later than usual at night in an attempt to allow delayed planes to take off.
The snafus occurred at the height of the ski season, with 69,363 passengers transiting through the airport, compared to a daily average of 40,000, according to airport figures.
Airport spokesman Stämpfli said of the 615 take-offs and landings scheduled for Saturday, 5.7 percent were cancelled.
He said the airport had never had so many unrelated incidents in a single day, ATS reported.