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In order to classify a project as failure or success, we first need to define project failure and project success. There is no easy way to define project success and failure as projects considered to be failure became success upon completion.
For instance Sydney Opera house can be a good example of success or failure debate. Times of over budget and over schedule but the end product made everyone say "wow", according to taxpayers the project is considered to be a big success but according to the executives the project is a major catastrophe as the project ran times of over budget and schedule.
Hence project success and project failure depends on the authority who decides it. Let's try to define project and project failure in the following topic.
Project Success & Project Failure:
There is no single definition for project failure and project success. Some of the standard and widely accepted definitions are as follows.
Definition 1: (Standish Group's Definition) 
According to Standish Group, a project is considered successful if the project met scope, time and cost (triple constraints). For example, if the project is to upgrade 500 desktops within three months for $300,000 then the project is successful if the work was completed in three months or less, the cost was $300,000 or less and all 500 upgraded computers met their scope.
According to Standish Croup a project is considered as a failure if it doesn't meet triple constraint and goes either over budget or over time or doesn't met or over met its scope or all of the above then it is considered as a failed project.
Definition 2: 
Even if triple constraints are met, the success of the project depends on the satisfaction of the stakeholders. A project which met its scope and completed under budget and under schedule could still not satisfy the stakeholders which according to them is defined as failure.
For example if the stakeholders and managers got help from the project team to solve critical project related problems, then satisfaction level increases. Even when project goes over budget and time if the customers are satisfied after completion then the project is considered to be a success by stakeholders. Hence a project not only required to meet triple constraints but also meet customer or stakeholder's satisfaction. For this reason many of the organizations implemented customer satisfaction rating system to measure project success instead of tracking triple constraints alone.
Definition 3: 
A project can be defined as successful if it met its initial objective, such as making or saving a certain amount of money, providing a good return of investment (ROI) or simply making the sponsors happy. The executive officers will be happy if the project provides good ROI even if the project crosses budget and time.
Let's consider the same example mentioned above, even if upgrading 500 computers takes more time than expected and it ran over budget, but it speeds up work and in turn increases profit then it makes sponsor happy who declares project as success.
Definition 4: 
A project can be defined as successful project if it is on budget and on time and meets its business value. That is,
Project Success = (on time + on budget) * business value
Where business value can be summarized in to cost reduction, business growth, maintaining operations and speed & efficiency
Project 1 - The London Ambulance System, 1992 
London Ambulance Service (LAS), one of the largest ambulance services in the world wanted decrease their response time, which forced them to drop the manual system and use automated IT systems.
LAS contracted the project to the consortium formed by Apricot Computers, Datatrak, and Systems Options (SO) to implement the project within 11 months for a budget of £937,463. Apricot computers and Datatrak supplied hardware while SO to develop the CAD Software.
The project was completed under budget and under time and implemented on October 26, 1992. First day after implementation system collapsed due to "overload" which claimed 46 lives and forced LAS to shift to manual system.
The project was completed under time and under budget and scope of the project was also met, but customer satisfaction was not good, the project didn't meet its initial objective as the application crashed and the business value of the project became almost zero. Based on the above definitions this project is classified under "failure".
Causes of failure:  
No proper quality assurance
Less budget & time frame
Lack of communication
Improper testing & implementation method
Lack of proper planning
Steps to be successful and lessons learnt:
Starting of the project didn't take place well as the timeframe and cost estimate was very low for a large project. Project planning was not efficient as there was no proper contingency and risk assessment in place, LAS removed manual systems moments before they installed IT systems solely depending on it. Communication was not up to the mark as there was no proper ownership of the project.
The project could be successful if there was proper Start, planning and continuous monitoring of the project.
Project 2 - Teton Dam, 1976 
U.S. Bureau of Reclamation (USBR) decided to build a dam on Teton River, three miles northeast of Newdale, Idaho to provide recreation, power generation, irrigation and flood control for the area under the shadow of the dam which is approximately 40,000 hectares.
The Office of Design and Construction, USBR designed the dam and the construction of dam was contracted to Morrison-Knudsen-Kiewit in December of 1971 for a budget of $100 Million. The construction began in February 1972. After four years of construction the damn was finally completed and started storing water from 3rd October 1975.
Between 10.30am to 11.55am on 5th of June 1976 the entire dam collapsed letting 80 billion gallons of water rushing out the dam, which flooded the four towns killing 12 and left 200 families homeless.
The project was completed under time and under budget and scope of the project was also met, but the objective of power generation, irrigation, "flood control" was not never met and the business value went to negative as the government spent $300 million in damage. Based on our definitions this project is classified as "failure".
Causes of failure:  
Poor design & construction
Lack of quality
Construction was not up to the design
Steps to be successful and lessons learnt:
The construction site picked by USBR was marked as a region with high volcanic rocks by the research group. The design developed by USBR had an arc which didn't distribute the water pressure equally; stress at some point was higher than others. And the quality of the materials used was also not up to the mark, evidence shows that fill soil used was wind-deposited non plastic to slightly plastic clayey silts, which are highly erodible.
This project could have been made success by proper planning (starting with choosing a site recommended by research group), having a proper quality check on the construction and materials used and before starting a construction project design should be verified for any faults.
Project 3 - New Wembley Stadium, 2006  
Wembley stadium was the home of English football for almost 80 years. Plans have been made by Wembley National Stadium Ltd (WNSL) to replace this iconic stadium to a brand new Wembley stadium with 90,000 seating.
WNSL contracted the project under fixed bid to Multiplex Constructions Ltd, for a total budget of £757 million to be completed by March 2006 for FA Cups. Multiplex constructions ltd was the main contractor, there was no sub contractor.
Construction started by October 2002, and ran around a year over schedule. Construction was completed by 2007 instead of actual completion date of March 2006. This resulted in cancellation of block of events in 2006 due to the construction delay. Multiplex was charged around £120,000 ever day over schedule. This made Multiplex face a huge loss of around £45 million.
The Arc took more time than anticipated by Multiplex, moreover the cost of steel increased during the course of the project hence it is a fixed bid Multiplex couldn't claim it from WNSL.
Even though the project ran over budget and time the stakeholders (tax payers) are very happy about the stadium as it become a iconic stadium and the initial objective and ROI was achieved 100% added to that there is considerable business growth. Hence the project can be classified as "Success"
Causes of success:
Design and Construction
Return of Investments
Even though the project was considered to be fiasco by media, after the completion of the project the benefits and objective of the projects are met. However the delay in the construction resulted in cancellations of events which led to loss of revenue and reputation.
The reason WNSL didn't face major loss was because the project was a fixed bid and since the initial objectives are met the project is considered as successful.