Essentially, I want to be able to, for example, use a unix shell in my browser to log into a cloud-based machine.
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Based on your comment to Kara, you might try Web Apps, where they have a
Whichever site you choose, you'll need to assemble a lot more detail if you want a meaningful response.
If you've already got the 'cloud machine' available, and you're just looking for commands/tools to accomplish this in unix, I'm going to go with the Unix SE site. If you also want to learn about how to set up the 'cloud machine' it's possible that serverfault can help you, but your question will need specifics about goals, limitations, etc.
Sorry - not much to go on, hopefully I'm not being overly simplistic.