Designing without research or exploration is probably a cardinal sin in someone's "How To Design Things" bible. I mean, you can probably bust out a pretty okay project without having done your "due diligence... but you're also missing the bulk of the fun.
Thoughtful and deliberate research promotes thoughtful and inspired ideation. Laying the foundation for your project early on with inspiration, focused direction, and new ideas will protect you from those frustrating moments later on when you don't even recognize what you're working on anymore. And of course, these websites aren't just for designers. A typographic treatment may inspire a photography series or a cleverly illustrated logo may lend itself to a stop-motion animation project.
Inspiration is everywhere. These just happen to be my favorite places.
That being said, every designer has their unique list of go-to resources. Print resources aside (look books, brochures, packaging, coffee table books), I've collected my personal top 5 resources for design inspiration. These items are always bookmarked on my browser bar and 80% of the time, I am using ALL these resources for a single project. I hope they become as useful for you as they are for me!
Pinterest - Ahh, the golden mecca of DIY and gluten-free recipes. I use Pinterest practically everyday. My most commonly searched keywords are "branding," "package design," and "logo design." It's not only a great resource for inspiration or discovering new ways to solve a problem. It's also a really nice way to see what other designers are doing, as far as organizing their brand work and what themes or trends are emerging.
Designspiration - Moodboards are, like, my most favorite thing ever. I pull a lot of "emotive" images from this site (and Flickr as well) to create a cohesive and focused moodboard for business and event branding. My two favorite things about this site are the "search by color" feature at the top of the page, where you can select one or multiple colors to generate an image search. Also, to search any keyword, you just start typing. Like. Just start typing and the search thing fills up the whole thing. It's cool.
Typewolf - This is actually pretty recent resource discovery. Personally, I'm still learning about the impact excellent typography can have. I know that a lot of us struggle with finding new uses for overused fonts or struggling to find fresh, new, applicable fonts that will last for some time. On every project, they show you a large sample of the completed work so you can see the type play in context. They also run monthly blog highlighting their favorites typographic sites and where to find/buy/download the fonts.
Design Seeds - There's an admirable integrity to spending a large portion of the design process sweating over the right Pantones or the right HEX code. When it comes to color, I like to rely on the excellent taste of those who have come before me. Founded by Jessica Colaluca in 2009, Design Seeds is an evergreen resource for gorgeous, natural palettes inspired by photography. Also, it's just freaking pretty to browse through.
Typographic Posters - Another recent find, Typographic Posters focuses on print/poster art. Obviously, this area of study is what intrigued me to start learning graphic design. When I was designing theatrical posters every week for a community college theatre productions, I was always trying to emulate certain styles. This site is a great way to kind of cleanse the palette if I'm buried too deep in something digital with a lot of whitespace. Overall, I think they're just super fun.
Of course, there are dozens of excellent resources hanging out there on the internet and in your local library or bookstore. And yes, I am a firm believer that it's necessary (and natural) to go out and actually touch some real books and magazines during your process.
I hope these resources help you with your next project!