I just looked at a few sites providing space related images for download. All images – except the logo’s from these three sites are freely useable for non-commercial purposes, including personal web sites – of course with a clear attribution of the source.
The three sites I looked up here are
NASA (of course)for general space travel and some astronomical images.
The Spitzer Space Telescope for images taken in infrared
and of course The Hubble Space Telescope with some of the most stunning astronomical images made
If you like images, maybe using them part of your web pages these are three very good sources.
Do not forget that many observatories and universities have images available. These include very old images from the classical telescopes in the world. I believe there is a project to scan all those ancient images before they are lost forever due to the deterioration pf the photographic material.
The old images *could* become important for detecting transient events or variable phenomena, like recurring nova outbursts, so we can not afford to lose these images.