Which common illness is primarily characterized by high fever and severe muscle pain?

Dengue fever is primarily characterized by high fever, severe muscle pain, and other symptoms such as joint pain, headache, and rash. The intense muscle and joint pain associated with dengue fever is often described as "breakbone fever" due to its debilitating nature. This illness is caused by the dengue virus, which is transmitted by mosquito bites, particularly from Aedes mosquitoes.

In contrast, the common cold typically presents with milder symptoms such as a runny nose, sore throat, and cough, without the severe muscle pain or high fever associated with dengue. Chronic fatigue syndrome is primarily characterized by persistent fatigue that is not improved by rest and may include other symptoms, but it does not present with high fever or severe muscle pain as its main characteristics. Allergic rhinitis, or hay fever, involves symptoms related to allergies, such as sneezing, itching, and nasal congestion, and does not involve fever or muscle pain at all.

Thus, dengue fever stands out among the options for its hallmark symptoms of high fever and severe muscle pain, making it the correct answer.