The definition of a rival: a person who is competing for the same object or goal as another, or who tries to equal or outdo another; a competitor.
Federer and Nadal may be rivals since 2006, but their rivalry is a friendly one, never getting in fights or anything of the kind.
I have always thought as Agassi and Sampras as more of "rivalry" than Federer and Nadal. They faced each other 35 times (Sampras leads all-time, 21-14), versus just 20 for the other two (13-7, Nadal).
Their battles were always intense as tennis and emotions were both high. Federer and Nadal, however, are always nice to each other, Nadal always reminds Federer of his number one ranking, even after wrecking him in 22 games in Paris.
Agassi and Sampras never had a player dominate as thoroughly as Nadal did at one point in 2008. They always fought until the end. They were compatriots, fighting for the love of their country. Federer and Nadal are probably the most recognized athletes in all of Switzerland and Spain, respectively.
The charity event in Indian Wells, "Hit for Haiti", perfectly proves my point. In a doubles match: Federer and Sampras versus Nadal and Agassi, Fed and Rafa watched in disbelief as the other two had a heated exchange.
After Sampras imitated Agassi's pigeon-toed walk, and Agassi made fun of Sampras never tipping enough, Sampras, who was supposed to serve to Nadal, smashed a serve right at Agassi.
The two got over it, and Agassi later apologized to Sampras, but this exchange made sure that this rivalry would never die.
Although forever linked, like Magic and Bird, Ali and Frazier, and of course Agassi and Sampras, Federer and Nadal are more of a friendly rivalry then the rivalries above. Agassi and Sampras are not friends, but actually true rivals.