Supabase

Supabase gives you a full Postgres database along with authentication, file storage, realtime updates and serverless functions. You can have a working backend in minutes, and since it is plain Postgres, you are never locked into a strange data model. For AI projects it supports vector search through pgvector, so you can store embeddings next to the rest of your data. It also offers an AI assistant in the dashboard that helps write SQL and design tables. Supabase has a generous free tier and paid plans that scale with usage. It is a favorite of indie developers and startups who want to move fast without giving up a real database.