Honestly, I have been a big proponent of the classic teams being better than today's teams in the LeBron/Heat vs 86 Celtics thread, but in my short lifetime (I only recently turned 20) the Spurs were the best basketball team I have ever seen as it was happening. With that being said, I think they have to be one of the top 5 teams ever.
For starters, their regular season was spectacular. 62 wins in what might have been the most competitive conference ever. And half the time the Spurs were barely even trying to win. No player on their team averaged more than 30 minutes per game (I believe they were the first team EVER to do that) and there were multiple occasions where the big 3 was completely rested for entire games. If they actually cared about winning every single game, I think they could have won 70 this season, it is seriously in play.
In addition, they ROLLED in the playoffs. For some reason, everyone is talking about the Dallas series again, talking about how it is a black mark on the Spurs season. As if taking 7 games to beat a 49 win team (49 wins in the ultra hard west) with a top 30 all time player, a great head coach and savvy talent across the board, was a bad thing. They then took a Portland team that played REALLY well against Houston and just ran them off the court. Next up was OKC, a team a lot of people thought was better. The Ibaka absence and then comeback was overblown, I still think San Antonio would have won the first two games easily even with Ibaka.
In the NBA finals, they took on the two time defending NBA champs in a series where everyone thought was a toss up. Instead, the Spurs throttled them to a historic level. No team in NBA history has ever had a more impressive finals, setting the all-time record for point differential, which is even crazier when you consider how even these two teams were going into the series.
Lastly, I'm going to go to something Simmons wrote in his book. Say whatever you want about him, but the guys knows his hoops history and does a great job of putting all the accomplishments into context. In his chapter about all-time great teams, he talks about their being three tiers of all-time great teams. The first tier was a team capturing it's first title. A bunch of guys who have never climbed the mountain finally reach the summit into the culmination of winning. They can be great, but because they haven't won yet, there is still a level of doubt. The second tier is for a Champion defending it's title. These are great teams that now they are great and will do anything to protect their throne. The third and most elusive tier is a great team playing with a Fuck You edge. This is a former champion, who, due to circumstances that took place before the season began, decided it was going to play the entire season pissed off, eventually steamrolling its way to the finals. The 86 Celtics were great because they were pissed off that they blew the 85 finals, so they came out and unleashed holy hell on the league. The 2014 Spurs are another perfect example, a great team, pissed off that they lost the title the previous year, then rolled through everybody. They even talked about how last years loss was fueling them all the time during the regular season. That was what made them truly so great, and turned them from a great team, to an all-time great team.