In English everyone has an accent because there is no standard English accent. There may be a standard AmE accent, BrE accent or even Aussie accent (standard Aussie accent ? well not too sure after all). But given that even in the US, which is more homogenous for pronucation than the UK, there is a quite big difference between a typical New Yorker, Californian or South-Eastern accent.
In languages like Italian, Spanish or Japanese, where the sounds are less numerous and more clearly defined, their may be dialects (different words) but hardly any accents (different pronuciation for the exact same word). If there is (like Kansai vs Tokyo accent) it's about the stress of the word (HAshi vs haSHI, etc.).
In other languages, there are accents, but one standard accent has been chosen so that any other accent can immediately be pointed out. French (of Europe, not Quebec) is the most obvious example.
To come back to the question, do I have an accent ? I am probably a special case given that I do not have one but many accents, which I can change voluntarily or which change according to my mood or the people I talk to. This is because I have learned many languages and strived to speak with the most "native-speaker" accent in each of them. So when asked to read a text in English, I can read it with a BrE accent (close to R.P., not BBC but more like Hugh Grant or Colin Firth), slight AmE accent (more California than New York), or French, Italian, German, Japanese, Chinese, Hindi accents or many other self-made accents not from any particular languages. My "natural" accent is none of them though, but depends a lot on my mood, and is closer to BrE spoken with a soft French voice (esp. when I am tired).