The logo I've created is all type. The type has been created in Adobe illustrator. I realise that it is vectorised already, but just need to clarify if the vector image is suitable for print outs scaling up/scaling down/using on a website?
I've found that for web, exporting from Illustrator as .svg gives excellent results. .JPG or .PNG will rasterize the image, which is usually fine, but .svg seems to provide a clearer, crisper image.
For print, @Lucian is correct, PDF is most common. If you need to provide a file to a screen printer or embroidery company for clothing, many times they will request the native .ai or .eps file. As with any project, discussing the project requirements ahead of time with your printer/web designer/etc. is beneficial and will likely prevent extra work.