When do we need to apply a software development methodology

First, it's not a choice of waterfall or agile, but plan-driven versus agile. There are many plan-driven methodologies to choose from. The other prominate plan-driven methodology is Boehm's Spiral Model. It's iterative development, but it's not (necessarily) incremental. I asked a question about other plan-driven methods, and the other one that was indicated was Cap Gemini SDM.

When you are deciding between a plan-driven methodology and an agile methodology, there are a number of factors to consider. In Rapid Development: Taming Wild Software Schedules, Steve McConnell has an entire section devoted to chosing a lifecycle model. He looks at a number of lifecycle models - pure waterfall, code-and-fix, spiral, modified waterfalls, evolutionary prototyping, staged delivery, evolutionary delivery, design-to-schedule, design-to-tools, and COTS software. Each is discussed in depth, and assessed on its ability to cope with poorly understood requirements, to produce a reliable system, to manage risk, to fit within a constrained schedule or budget, to provide visibility to customers and/or management, and the sophistication of the team.

So, yes, one consideration is the type of project that is being delivered. But there are numerous factors and many lifecycle models that can be chosen from.

SCRUM is a general purpose methodology that can work well for most projects and team sizes, but is less useful for large teams that do very large projects. The sheer number of people involved on some projects makes any agile methodology extremely difficult to near impossible because a more rigid structure is required to keep order. The aerospace industry is a good example of an industry that tends to have huge projects where agile approaches aren't always feasible.