The DfE document describing the GCSE Mathematics subject content is an excellent starting point for checking new content, all exam boards must include this content.
Note that only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content. See page 4 of the DfE document.
There are many excellent resources for teaching Venn Diagrams; investigate this collection.
On Diagnostic Questions – Probability with Venn Diagrams.
Diagnostic questions now has over 21000 questions on Mathematics including wonderful collections of examination questions. The site is completely free (and promises to remain so). Plenty of help is available to help you learn how to use the site.
CIMT is one of my Top >10 websites for a very good reason – when I want additional examples for any topic at any level I can always find them on CIMT! Venn Diagrams are no exception to this, you can find Sets and Venn Diagrams, Set Notation and Logic and Venn Diagrams in the student interactive resources and the text chapter on Logic from the Year 7 text here; in sections 1.3, 1.4 and 1.5 of the text you will find examples and exercises on Set Notation and Venn diagrams. See also the additional Teacher resources for this unit (Unit 1, Logic) such as Additional exercises are also available as are Aural Tests. Other teacher resources include slides and Revision Tests (you will need the CIMT password for the Revision Tests).
From AQA’s excellent Bridging the Gap resources, Sets and Venn Diagrams is superb, also see the OCR resources, from OCR’s Check In tests, see Combined events and probability diagrams. For further information on the changes to Probability at GCSE see this post.
From Transum try Venn Totals. 4 different levels of exercises which can be checked are available. Level 1 – Reading information from a Venn diagram containing two intersecting sets. Level 2 – Reading information from a Venn diagram containing three intersecting sets. Level 3 – Adding information to a Venn diagram containing three intersecting sets. Level 4 – Adding information to a Venn diagram containing three intersecting sets with some problem solving required. There are also exam style questions, to see the worked solutions a subscription is required.
From Sums Mathematics come two very useful activities to illustrate Venn Diagrams. From the Index choose Sorting & dbases under Data Handling where you will find Venn Diagram activities for two sets and three sets.
From teachitMaths, try Venn diagram dominoes (pdf versions of all the resources on this site are free).
From Craig Barton – see this whole collection of rich tasks with Venn diagrams.
To really challenge your students combine Venn Diagrams and Algebra and try this review question from Underground Mathematics. (From a 1969 MEI O Level Additional Mathematics paper.
A search finds more problems – all resources on Underground Mathematics include complete documentation including suggestions, a full solution, printable materials and more.
Perhaps try Can we find how many boys study French, Latin and German? or Quadratic Solving Sorter – not a traditional Venn diagram problem but certainly a diagram as in the possible solution presented is a very good idea.
From Census at School combine Statistics and Venn diagrams, and check this task on Washing Up!
With the Triple Venn Diagram Shape Sorter you can either set the rules or guess the rules by selecting the appropriate botton:
Some excellent activities are available from the Illuminations site.
The Shape Sorter allows exploration of geometric properties of shapes.
Select Instructions and Exploration for clear information on how to use the resource.
On a lighter note – a Twitter conversation on a fun idea!
If you want to create your own there are plenty of tools to use – there is a good summary here on Cometdocs.
…and to take Venn Diagrams to their extremes have a look at these wonderful images from New Scientist!