None of these are free trials or free credits. Really free forever, and not limited enough to be useful. This is by no means a complete list. Just services I think are useful and cool.
Besides hosting git repositories for storing code, and collaborating on projects (alternative: GitLab), Github offers Github Pages for static website hosting.
Also offers a Github Student Pack for students, with some good offers.
Good for playing around with code in basically any language.
Can host basically anything that doesn't exceed its hardware limits. Bots, websites, etc.
Open a webserver in the repl, and have UptimeRobot ping it, to keep it alive.
Free tier: Unlimited public repls with 1 GiB of storage, 0.5 vCPUs, and 1 GiB of RAM, EACH
Monitors uptime of websites and other services. Can notify you when something goes down, and also tracks response time.
Free tier: 5 minute monitoring interval, 50 monitors (more than you need)
Good to mock up and share web frontend stuff (HTML, CSS, JS, etc).
Cloudflare has an incredibly generous free plan, and is basically a must have for managing websites. DNS (and DNS proxying), forwarding email, ddos protection, basic analytics, SSL, it basically has everything you need.
Gives a free tier cluster for each project (so you can have multiple free tier DB clusters). MongoDB's libraries are also great to work with.
MongoDB has a collection and document based system (alternative: Firebase for JSON based [not recommended. firebase sucks], ElephantDB for SQL based).
Free tier cluster gives you: 1 M0 (shared) cluster per project, which has 512 MB of storage (half a GiB)
Like MongoDB, but for PostgreSQL.
Free tier gives you: DB with 20 MB data and max of 5 concurrent connections
Secure and free captcha service (unlike recaptcha...). However, can be bypassed with an accessibility cookie.
Reverse proxy that can tunnel TCP, HTTP, and TLS traffic. Good for making a locally running website/app accessible to the internet, without too much hassle.
Free tier: 1 free tunnel, but address changes every tunnel restart
Google sucks, but at least they give you access to a huge library of fonts (can hotlink or download).
Don't forget free and open source software! For example, GIMP is great for image editing, and inkscape is great for making graphics.