KV caches, typically used only to speed up autoregressive decoding, encode contextual information that can be reused for downstream tasks at no extra cost. We propose treating the KV cache as a lightweight representation, eliminating the need to recompute or store full hidden states. Despite being weaker than dedicated embeddings, KV-derived representations are shown to be sufficient for two key applications: \textbf{(i) Chain-of-Embedding}, where they achieve competitive or superior performance on Llama-3.1-8B-Instruct and Qwen2-7B-Instruct; and \textbf{(ii) Fast/Slow Thinking Switching}, where they enable adaptive reasoning on Qwen3-8B and DeepSeek-R1-Distil-Qwen-14B, reducing token generation by up to $5.7\times$ with minimal accuracy loss. Our findings establish KV caches as a free, effective substrate for sampling and reasoning, opening new directions for representation reuse in LLM inference. Code: https://github.com/cmd2001/ICLR2026_KV-Embedding.