Interesting question. First, a little diversion into history. The genesis of playing cards is still a hotly debated subject and far too involved to discuss here, but it's generally accepted that modern cards trace their origin to central Asia, well over 1,000 years ago. Four-suited decks with court cards evolved in the Moslem world, and spread to Europe in the late 1300s from there.
What had initially been hand-painted luxury items became mass-produced with the invention of woodcuts (in fact, it's been suggested that demand for playing cards was significantly responsible for the development of the printing process). The familiar four suits of spades, hearts, clubs, and diamonds, as used in English and American decks today, derive from the original French design. (Note: It's the design that's distinctly French; the meanings behind the symbols probably originate in Spain -- see below.) The reason for the French symbols' spread was their simplicity -- those solid monochrome characters could be mass-produced using a stencil, with only the court cards requiring printing. Elsewhere in Europe, different suit symbols evolved and are still in use today, including hearts, leaves, bells, and acorns in Germany, and coins, cups, swords, and batons in Spain and Italy, but these more complex designs could only be accurately reproduced using woodcuts.
Returning to the question at hand, the answer is that in poker in the United States, there generally is no ranking, so if two hands tie with a royal flush, the pot is split down the middle. The only time that suits are sometimes ascribed an order of rank is in the settling of minor issues, such as who deals first or what game to play. If two players both draw cards of the same rank, the tie can be broken by using an arbitrary hierarchy system. Two common conventions are 1) alternating colors, with diamonds considered lowest and spades highest, or 2) an alphabetical ordering beginning with clubs as lowest.
This second ranking system is also the one employed in the game of bridge, where suits do matter, and corresponds to the meaning behind the original Spanish suits, which reflected the four major divisions of medieval society: spades (originally swords, denoting nobility -- the highest rank); hearts (clergy), diamonds (merchants), and clubs/cudgels (peasants -- the lowest). The game of hearts uses this same suit ranking. Other games, including skat and five hundred, employ different systems.
So does Italian poker, apparently, where the ranking of hearts (high), diamonds, clubs, and spades is used to break ties between otherwise equal hands. That's the only instance we've come across of poker employing a system like this to determine winning hands. If anyone knows more about this or other examples, please let us know.