For this question, let's assume the contract is for common goods and services.
First hypothetical scenario: I meet a plumber on an online marketplace, like Facebook or Craigslist, and he writes that he will fix a problem in my bathroom. He guarantees that he will pay for any unexpected damages that might happen during the repairs.
Second hypothetical scenario: I hire a local graphic designer to create a logo for my new business. In an email, the designer agrees to transfer all copyright claims to the work once they have been paid. This agreement is made through email, not a signed written agreement.
Are the promises made in either of these cases legally binding?