What is plagiarism in design and what is not?

"The secret to creativity is knowing how to hide your sources."
Albert Einstein   

"Good Designers Copy, Great Designers Steal"
Pablo Picasso   

"Nothing is original"
Jim Jarmusch , an American independent filmmaker  

One of the steps to becoming a good designer is to learn from the works of professionals. They should serve as inspiration for you, or if you are stuck, and not sure what to do. It is one of the necessities for a successful graphic design solution to search and analyze the best design works, and use one as a guide for your design.
Working on a project as an inexperienced designer, do not try to find an idea in your head (it doesn't have any yet), search for them. Starting to search, do not use the first one that you find, you should spend at least several hours looking at images, or colors, or layout, or font, or…, till you say: “I think it looks very similar to my idea!”
You cannot be a good designer from day one. Time is needed to sponge up information from different sources around you, and the first place to look - works of the highest quality. The search for inspirations and ideas is an investment. After all, the time you spend searching will be rewarding for you. You will spend a lot more time if you try to work using your own “experience” and then redoing it 100 times because your client would not like it (unless you are a professional designer).
In a while you will learn how to find ideas for your design from anything that you see around.

ADVICES OF HOW TO FIND INSPIRATION
10 Unusual Places to Get Design Inspiration (advices down the page)
Here is a very good poster that illustrates this idea:

Compare the shelf with books and a design underneath
(an advertisement of CorelDRAW software)

You should not confuse plagiarism and using good design as a guide for your work. Plagiarism is when you copy somebody’s work and say that it is yours. But using some design as a guide, means that you adapt one, at most two elements for your work (for example, colors).
So, while you do not have design experience yet, to create a good design you need to find a work that inspires you, emulate it, and then make some alteration, so that work becomes unrecognizable.

Even looking at the works of talented and famous designers, or just searching on the Internet, you can say: "Oh, I have seen a very similar design, so it is plagiarism!"
But it is not always the case. For example, it can be a simple coincidence because we live in the same time, looking at the same images, hearing the same sounds… and reinventing the wheel all over again.

This is a flyer that I made before I saw these Newport and Game Tap ads (please ignore this awful font face, it was many years ago)

Sometimes these similarities are intentional, so called HOMAGE.
Homage - special honor or respect shown publicly. Homage pronunciation

Here are several examples of homage and inspiration:
Las Meninas, Velazquez
Las Meninas, Picasso
Las Meninas, Dali

Some more:
                       
           

This is very interesting posters collection: http://www.artlebedev.com/mandership/154
Although, in the author’s opinion, these posters are disrespectful, the point here is the similarity between all of them.

PLAGIARISM EXAMPLES:

               

CAN BE CONFUSING:
Sometime it is difficult to differentiate what is of plagiarism, what is homage and what is work created by inspiration (you decide what is what):
Graphic Design Rips Offs or Inspiration? (read the comments too)