Can anyone please tell which Image Hosting sites don't allow peers to download image.?

Flickr & DeviantArt both offer the option to add an invisible layer image over your uploaded image, so any user who right clicks or drags the image to the address bar only gets the layer image and not the real one, they're probably the best choices.

If you know what you're doing, you can easily save an image regardless. It's not as easy, but there's always a way around the limitation.

You could watermark the image then you could tell if anyone steals it.

Use something like GIMP to add an opaque layer to the image with your name wrote across it so people can still see the image but would struggle even with the print screen method to remove the watermark.

Flickr gives you the option to "spaceball" your image. Meaning nobody can save it and if they try to, they will get a blank .GIF

Of course, there are always ways around it like screencapping and then copypasta into photoshop, but it's as close as you can get to being secure. (There's ALWAYS a way around security on the internet. No avoiding this fact)