Whenever you need to post an image on your blog, you will need to upload a photo to blogger directly. That however does not give you much freedom to work with the image and even renaming the image is not quite possible. It is therefore recommended to have a Image Hosting account for use with your blog. The good news is that there are many free image hosting providers that give you good features at absolutely no cost. My personal favourite is Photobucket, but below is a list of other free image hosting providers that you can use to post images on your blog. Many of them are now allowing free video hosting as well. Some of them will not require you to register with them too.
http://photobucket.com ( Images + Videos )
http://www.imagecabin.com/ ( Images + Videos +MP3 & more.. )
http://tinypic.com/ ( Images + Videos ) 
http://imageshack.us/ ( Images + Videos )
http://allyoucanupload.webshots.com/ ( Images )
http://www.freeimagehosting.net/ ( Images ) 
http://www.theimagehosting.com/ ( Images )
http://www.imagevenue.com/ ( Images )
http://www.piclynk.com/ ( Images )
http://www.filehigh.com/ ( Images + Videos + Cursors )
http://www.theimageplace.net/ ( Images )
http://www.imgplace.com/ ( Images )
http://xs.to/ ( Images )
http://www.myonlineimages.com/ ( Images + Videos + ZIP & more.. )