Here is a description of a few of the popular use cases for Apache Kafka. For an overview of a number of these areas in action, see this paper.
Messaging
Kafka works well as a replacement for a more traditional message broker. Message brokers are used for a variety of reasons (to decouple processing from data producers, to buffer unprocessed messages, etc). In comparison to most messaging systems Kafka has better throughput, built-in partitioning, replication, and fault-tolerance which makes it a good solution for large scale message processing applications.
In our experience messaging uses are often comparatively low-throughput, but may require low end-to-end latency and often depend on the strong durability guarantees Kafka provides.
Website Activity Tracking
The original use case for Kafka was to be able to rebuild a user activity tracking pipeline as a set of real-time publish-subscribe feeds. This means site activity (page views, searches, or other actions users may take) is published to central topics with one topic per activity type. These feeds are available for subscription for a range of use cases including real-time processing, real-time monitoring, and loading into Hadoop or offline data warehousing systems for offline processing and reporting.
Activity tracking is often very high volume as many activity messages are generated for each user page view.
Metrics
Kafka is often used for operation monitoring data pipelines. This involves aggregating statistics from distributed applications to produce centralized feeds of operational data.
Log Aggregation
Many people use Kafka as a replacement for a log aggregation solution. Log aggregation typically collects physical log files off servers and puts them in a central place (a file server or HDFS perhaps) for processing. Kafka abstracts away the details of files and gives a cleaner abstraction of log or event data as a stream of messages. This allows for lower-latency processing and easier support for multiple data sources and distributed data consumption.
In comparison to log-centric systems like Scribe or Flume, Kafka offers equally good performance, stronger durability guarantees due to replication, and much lower end-to-end latency.
Stream Processing
Many users end up doing stage-wise processing of data where data is consumed from topics of raw data and then aggregated, enriched, or otherwise transformed into new Kafka topics for further consumption. For example a processing flow for article recommendation might crawl article content from RSS feeds and publish it to an "articles" topic; further processing might help normalize or deduplicate this content to a topic of cleaned article content; a final stage might attempt to match this content to users. This creates a graph of real-time data flow out of the individual topics. The Storm framework is one popular way for implementing some of these transformations.