RNNs can be categorized based on the relationship between the input and output sequences. Here are some commonly used types:

1. One-to-One: The simplest type, where a single input is mapped to a single output, similar to a traditional feedforward neural network.

2. One-to-Many: In this type, a single input is mapped to a sequence of outputs. For example, generating multiple words from a single image caption.

3. Many-to-One: In many-to-one RNNs, a sequence of inputs is mapped to a single output. For example, sentiment analysis, where a sentence is classified as positive or negative.

4. Many-to-Many (Same Length): Also known as sequence-to-sequence, these RNNs take a sequence as input and produce a sequence of the same length as output. Examples include machine translation or image captioning.

5. Many-to-Many (Different Lengths): In this type, the input sequence and output sequence have different lengths. An example is video classification, where an input video is classified frame by frame.

These different types of RNN architectures allow flexibility in handling different input-output relationships, making them suitable for a wide range of tasks involving sequential data.