Assessment: oh no not another essay

A survey of written assignments in British higher education, for an ESRC project, helpfully lists 12 "genres" of student writing - useful for broadening your ideas if you're trying to design an assessment task:

• Case study: A description of a particular case with suggestions for future action, to understand professional practice (eg in business, medicine, or engineering).
• Critique: A description, explanation and evaluation to show understanding of the object of study and to show ability to assess its importance.
• Design specification: An explanation of the design of an item, including its purpose, parts, development and any testing of parts and procedures.
• Empathy writing: A letter, newspaper article or similar non-academic genre showing understanding and appreciation of the relevance of academic ideas by adapting them for a non-specialist readership.
• Essay: A piece of writing showing writer's ability to argue coherently and develop thinking and critical skills.
• Exercise: Data analysis or a series of responses to questions, to provide practice in key skills and to show knowledge of key concepts.
• Explanation: A descriptive account and explanation to show understanding of the object of study and ability to describe and/or assess its significance.
• Literature survey: A summary to show familiarity with literature relevant to the focus of study and ability to assess its place in literature generally.
• Methodology recount: A description of procedures undertaken by the writer, possibly including Introduction, Methods, Results, and Discussion, written to develop familiarity with disciplinary methods, and to record experimental findings.
• Narrative recount: A fictional or factual recount of events to develop awareness of motives and/or the behaviour of organisations or individuals (including oneself).
• Problem question: A text presenting relevant arguments around a problem, written to practise application of specific methods in response to simulated professional scenarios.
• Proposal: A text including an expression of purpose, a detailed plan, and a persuasive argument to demonstrate ability to make a case for future action.
• Research report: A text often including Literature Review, Methods, Findings, and Discussion, or several 'chapters' relating to the same theme, written to demonstrate ability to undertake a complete piece of research, including research design, and to appreciate its significance in the field.

More details, with examples from a variety of subjects, are in Table 4 (pp 23-26) of the full report (accessible from the link above).