If you're looking for a very simple image host that doesn't mess around with what it has to offer, I'd say that ImgBox.com is probably the way to go. This place has a simple button in the middle of the screen that allows you to select your files: it also has drag and drop capabilities, which a number of competitive services do not boast.
On the plus side, files here can go up to 10 MB in size and JPEG, PNG and GIF find support. On the negative side, there is no format switch that makes GIFs into HTML5 videos.
You'll also find that Img Box has gallery support and the ability for you to delete the material you've shared without signing in (so long as you keep the link required to do so handy). Img Box is actually a very neat site and competes as one of the best on the web. You will have to identify the material as being adult in nature, though: that to me is the only real problem that I wish they'd do away with.