Depending on the type of media, if it is collaborative and if I want to share it: I start with Pinterest, Are.na or a blank artboard in XD.
1. Pinterest: Easy way to get started collecting images and videos.
Pros: Easy to collaborate and share pictures/videos. Cons: It is frustrating if you want to organize into subcategories, you can't merge boards, and the tagging/search UX is a mess. Honestly who writes the descriptions for these things?
2. Are.na: Great for in-depth research.
Pros: Are.na has the ability to collect all types of media for inspiration (including website captures). Cons: It might be overkill and a time-suck if you just want to create a simple visual moodboard.
3. Artboards in XD, Sketch or Keynote.
Pros: No fussing with UI, no broken links, no ads, no need for an internet connection. Best for quick and dirty moodboarding, which I honestly find to be useful for capturing the essence of a vision. It's also easy to subdivide different aesthetic directions. It's easy to create your own templates using clipping masks. Cons: You can only blame yourself for this mess.
4. Magazines, printouts and foam-core boards.
Pros: This can be fun and inspiring if you have relevant resources (but do you really want to sacrifice your precious copies of Apartamento to the analog Gods?) Cons: Limitations, glue sticks and storage problems. This can be an emotionally stunting disaster where you end up crying on the floor surrounded by shredded bits of paper and bitter memories of middle school. Nostalgia can be a double-edged sword.