More than half of the 650 sessions are already oversubscribed after last-minute surge on website
London 2012 organisers said they were "thrilled" after revealing they had received applications for more than 20m Olympics tickets during the first phase of sales.
More than half of the 650 sessions are already oversubscribed at the end of the first round of ticket sales, with track cycling, rhythmic gymnastics, triathlon and the equestrian cross country among the first sports to sell out.
After a last-minute surge in applications that caused the website to slow to a crawl and forced a last-ditch extension of the deadline early on Wednesday, the London organising committee (Locog) said 1.8 million people had submitted applications for the 6.6m tickets available to the public.
Locog also confirmed that anyone who had not applied for tickets in the initial 42-day phase would not get the chance to do so until much later this year. Instead, those applicants who have received none or only some of the tickets for which they bid will be offered further opportunities in June and July to apply for other events.
The opening ceremony, for which tickets range from £20.12 to £2,012, was the most popular event and was more than 10 times oversubscribed. Successful applicants will have money taken from their accounts between 10 May and 10 June and will be notified which tickets they will receive before 24 June.
That has drawn criticism from some consumer groups, which claim the system tilted the scales in favour of those able to rack up a large potential bill in the hope of securing the most sought-after tickets.
Track cycling, in which Team GB won an unprecedented eight gold medals in Beijing, was always expected to be among the hottest tickets, as were the opening and closing ceremonies.
But some of the other sports to sell out are more surprising. They include rhythmic gymnastics, modern pentathlon, the cross country equestrian events in Greenwich Park and the triathlon in Hyde Park. All have a committed following, a limited number of sessions and tend to be reasonably priced. Locog said that most swimming and tennis sessions had also sold out.
Lord Coe, the chairman of Locog, said: "We are thrilled with the response right across the board, in all sports and all sessions. What is most encouraging is that the majority of applications are for multiple tickets and for several sports, which shows that friends and family are planning to go to the games together."
Locog did not reveal which sports have the most spaces remaining, though tickets for those with lots of sessions in relatively large venues will inevitably be among the most difficult to shift. They include volleyball, football, basketball and handball.
There was also criticism of the technology underpinning the ticketing process from some who claimed they were unable to access the site in the hours running up to the midnight deadline.
Locog said the site was overburdened for only 20 minutes, but some users reported being unable to process their orders for two hours or more. Locog, which extended the deadline to 1am, said all those who kept trying were eventually able to process their order.
Andreas Edler, managing director of a web hosting company Hostway UK, said: "Irrespective of the sudden late surge of demand, you would expect ticketing websites in this day and age to build in adequate capacity and utilise better traffic management practices to cope with the excess of visitors."