Useful resources for images
You may have already come across Unsplash as it's growing in popularity due to its beautiful, free, high quality images. You will definitely have seen some of their photos if you've every been on social media.
The search functionality is really good as users in the Unsplash community go through and tag them, plus people put together curated collections around particular topics.
Great for artsy or nature photos in particular. Or if you'e making a website where the subject is San Franciso hipsters.
If you're not finding what you need on Unsplash then Pixabay have a wider selection (including some photos from Unsplash) particularly if you're looking for anything a bit more corporate.
You'll sometimes have to sort through some rubbish images to find good ones, and you will definitely want to set the filter to just display photos, unless you're feeling nostalgic about 90s style clipart.
The Noun Project
Focusing on icons rather than photographs, The Noun Project has an ambitious aim to create a visual representation of every noun in the English language. This is a particularly useful resource for creating favicons and on the pro version you can even customise the icon to your client's brand colour before you download it.
To use the icons for free, you have to credit the author; or if you prefer to use the icons without a care in the world you can subscribe for $9.99 (which is what I do).