Just as with music, photos are also protected by copyright, and because you own your photos, there's no question you can put them on your website without violating copyright. But, when it comes to model releases, the question of "private use versus distribution" requires looking at other factors. As usual, we return to use. Because the ability to sell photos in editorial contexts without a release permits unreleased photos, you are allowed to display them as such. Where it can get sticky for pro photographers is whether the photos can be construed as being a form of advertisement, or advocating a political or religious position. This can be a problem for photographers who specialize in certain kinds of industries, like religious photos or political stock photography. The more specific you are, the more risk you assume. The more general you are, the safer you tend to be.
It has been questioned whether photos on a website constitute a form of self-promotion (i.e., advertising) because your site is something like a portfolio. Yet, this has never been tested in court, so at this point, it's merely conjecture. That said, it's another question of where along the spectrum a website may lie if it portrays images: is it a portfolio, or are you presenting material in an editorial context, or are you making photos available for use by editorial clients that do not need releases to license? Until a true precedent is established, I would assume that eventually a judge is going to look at cases individually and decide independently based on context.
