I've tried several. It's mostly for my own and open source projects with up to 10 users. I can't speak for big teams.

• Self-hosted without special service, just ssh and git. Worked pretty well for solo projects, but sharing and backups were a pain.
• Bitbucket (free) worked pretty well. It has most features but overall for some reason I find it slightly less smooth to work with than Github. But it works quite well and I still have some old projects on there that get pull requests sometimes.
• I had a self-hosted Githlab for one or two years. Gitlab itself is nice, but the self-hosting thing didn't work - it'd stop working after updates several times a year, and then I'd have to spend several hours fixing it.
• Github (free) works well for open-source projects. Most open-source projects in the world are on here it seems, and it is very polished and complete. I've started all my new open source projects here some years now.
• Github (paid) is similar but allows private repos. I moved the self-hosted private repos here, and also use it for small teams sometimes.
• I also had a look at COGS as a self-hosted solution. It seemed simple but I never ended up installing it because I moved to paid Github.

So basically for individual developers, I recommend Github.

I'm using a self-hosted Gitea instance. It is nice and has the same API as Github. I like it.

What service is the monkey icon for?

I have used these more popular ones:

GitHub: I don't get the popularity of GitHub outside of open source projects since I've usually looked for private repos. It has a good interface. I just wouldn't pay for the private repos if I can get them with the below services.

BitBucket: I like their service. Free repositories and backed by a company that's been around for a while and offers other development services. Not the best UI. The UI is kind of slow but overall easy to understand and navigate.

VisualStudio (VSTS): Also free private repos. Pretty good features, but I find the interface and features to be overkill for me. I've used their CI/CD service with success. UI is sort of what you might expect from Microsoft. They are rolling out a new UI that might be better.

GitLab: Also free private repos. I tried out the CI/CD service and it was easy to set up and worked well. The interface is also the most responsive out of all of these in my opinion.

I think that if I were starting from scratch and wanted hosted private repos I would go with GitLab first then BitBucket or VSTS then GitHub.