I'll venture to define a strong era:
An era can be called strong when there are two or more great players (5+ career GS titles) playing, all in their GS-winning, prime time (between each player's 1st and last GS title).
Using this definition, in this century, strong years include:
2000-02, Sampras, Agassi
2003, Agassi, Federer
2005-07, Federer, Nadal
2008-12, Federer, Nadal, Djokovic (This is the strongest era of this century. It could extend to when Federer wins another GS.)
2013-14, Nadal, Djokovic
2015 is not a strong year unless Fedal win another GS, or Stan or Murray win 3+ more GS.
I disagree, you only look for the presence of famous name without looking for their actual level of play. At the same time you remove players who have won only a few slams, as if because their total of slams isn't 8 or more, their level of play when they actually won these slams can't be higher that all time great players. Guess what. Safin and Hewitt creamed Sampras in the USO final, when they were 20 years old. Del Potro did the same with Nadal and Federer. Wawrinka played obviously at a more than decent level to win the AO and RG.
In my opinion, 2000 was a good year, with Sampras, Kuerten, Agassi and Kafelnikov, and younger players like Hewitt and Safin coming.
2001-2002 were pretty bad, as top players were very up and down with Sampras, Agassi, Hewitt, Safin, etc.
2003 was better with Roddick, Federer, Ferrero and Agassi, Nalbandian fighting each other.
2004-2005 were great with Federer peaking, Hewitt back, Safin, Roddick still blasting his forehand, Agassi for his last years, Coria, and obviously young Nadal.
2006 is weaker. Safin, Hewitt, Roddick, Coria, Agassi let a void to be filled with Ljubicic, Blake, Robredo, Davydenko, etc. At least these players were really in form at the time. Baghdatis seemingly was showing great promise and everyone was exited with him. Davydenko was already a very good player, his SF against Nadal in Rome is one of my favorite clay court match.
2007-2009 were great years. Federer and Nadal had some health issue but overall with the rising of Djokovic and Murray, some surge from other players like Nalbandian, Davydenko, Gonzalez, Del Potro, Verdasco, Soderling...
2010 was terrible until the USO, with most players having a slump or injuries. Davydenko and Del Potro got injured just when it seemed they were going to take another dimension. Djokovic and Federer didn't wake up until the fall season.
2011-2012 were great years, with Djokovic, Nadal, Federer, Murray all in good forms. These are the true big 4 years.
2013 was a classic duopoly with Nadal and Djokovic, not much to see outside of them.
2014-2015 are pretty much weaker years. Murray lost Lendl, he injured himself, and while he recovered quiet well, he forgot his forehand. Nadal has been declining a lot during these two years. Federer has surge and is nice to watch but in term of level of play he is far below what he showed in 2011-2012, let alone 10 years ago. Outside these players, Wawrinka is the only one to save the day when he is on. Djokovic is great but he has a red carpet to display his talent, very much like Fed had in 2006 and Nadal had in 2010.