For those whose native language is not English: what is an English-speaker's accent like when he/she speaks your language?

People who have learned English very often have an easily-detected accent (French, German, Indian, or what have you). When I'm learning a language, proper pronunciation is of course something I strive for, but I can't help but suspect that when I speak another language (e.g. French), a native speaker would be able to hear an accent in my speech. What I'm wondering is how an English-speaker's accent manifests itself in other languages. I realize this might be a difficult answer to articulate, but hopefully somebody can provide some insight for me. :)