Llama 2, from Meta, is a powerful language model that is free for both research and commercial use. It's available both as a raw pretrained model and, fine-tuned, as Llama-2-chat for conversation and Code Llama for code completion. Since it's available in a variety of sizes — 7B, 13B, and 70B — Llama 2 is a good option for a self-hosted LLM, if you want to control your data.
Meta describes Llama 2 as "open source," a claim that has attracted some criticism. Meta's license and acceptable use policy put restrictions on commercial use for some users and also restricts the use of the model and software for certain purposes. The Llama 2 training data is not open, which can hamper the ability to understand and change the model. That said, the availability of a powerful, capable model in at least a "semi-open" form is welcome.