There are a couple of signs that indicate when running a spike might be valuable:

The team finds it difficult to define clearly or agree on a suitable design or approach and discussion drags on without consensus.

People are reluctant or unwilling to estimate a piece of work, inflate their estimates, or there is a large range in the estimates given.

The system is about to move into a new area and/or a substantial change is forecast.

An issue due to a current design limitation surfaces.

A team member is convinced there is a better way of doing something but the wider team has not bought in.

Discussion is vague, generalizations abound and the conversation lacks data or concrete examples.

via Using Spikes.