What is the maximum memory a Google App Engine app may consume?

The maximum amount of local memory is not documented.

speculation:
I believe they have not imposed any hard limits because it may depend on your application traffic/load/activity and by other GAE applications.

There's an open issue MemoryError undocumented/hard to predict that you might want to star.

EDIT:
Reading the new Backends documentation here it seems capped to 128MB

The maximum memory limit for an App Engine instance depends on the instance class that you choose. The default limit is 128 MB. The following classes are currently available:

• F1 and B1 - 128 MB
• F2 and B2 - 256 MB
• F4 and B4 - 512 MB
• F4_1G, B4_1G - 1024 MB

Edit: Second generation instances have double the memory:

• F1 and B1 - 256 MB
• F2 and B2 - 512 MB
• F4 and B4 - 1024 MB
• F4_HIGHMEM and B4_HIGHMEM - 2048 MB
• B8 - 2048 MB