Visit this site for a general guide - bearing in mind everyone does things differently, but ALL the examples show on that page work well with 1) responsive designs 2) 960 grid 3) common screen resolutions 4) common branding and marketing logos in print or offline media complimenting a web site, all things one might consider when choosing a format.
If you were expecting ONE answer, anywhere between 760 and 900px wide with a height around 250-300 to start for sites 960-980px wide which seems popular these days. Maintain the aspect ratio using a graphics tool like Adobe PSD or similar, i.e. contrain proportions when image resizing.