What do Americans think of using 'cheers' to sign off an email?

Solution 1:

To me, as an American, it doesn't really get interpreted other than to flag to me that the writer is speaking British English. I have no idea when it is or is not proper to use "cheers" in British English, so it sort of gets ignored as to whether this is a formal or informal way of signing off.

Internationally, it's probably best to stick to a more formal "Thank you" or "I look forward to your reply" if the communication is with someone with whom you do not have a pre-established relationship. This is more important when the recipient is not a native speaker of English and may be confused.

Solution 2:

As an American English native speaker, I interpret it as "Thanks/Have a great day from someone from England (or possibly Australia)". Not that they were intending the "from England" part - that is just my interpretation.

Edit: I do find myself using it sometimes lately :) Also 'no worries', but I have some Australian friends, so I probably picked it up from them.

Solution 3:

As reported from the NOAD (New Oxford American Dictionary) the definition of cheers is the following:

cheers /tʃɪ(ə)rz/
exclamation informal
expressing good wishes, in particular
• good wishes before drinking: “Cheers,” she said, raising her glass.
• [British] good wishes on parting or ending a conversation: Cheers, Jack, see you later.
• [chiefly British] gratitude or acknowledgment for something: Billy tossed him the key. “Cheers, pal.”

Cheers is therefore used to express good wishes in both American English and British English; it's probably understood to have that meaning in a specific context (e.g., before drinking).
I would use good wishes.

Solution 4:

I am an American English native speaker, but I've been exposed to the British usage so much that I've ended a couple of emails with it myself. It always seemed like a fairly reasonable signoff.