Since 1980, 40 out of 45 NBA champions have had a Top pick in the draft, except

Since 1980, 30 out of 35 NBA champions have had a Top pick in the draft, except

Nowitzki 2011 (but he had two #2 picks...Chandler and Kidd)
Garnett/Pierce/Allen in 2008
Kobe 2010, 11
Detroit 2004

Note had Kwame Brown not been picked then Chandler and Gasol go #1 and 2 to take three more titles off this list

Here's further exceptions due to NBA rules or two players in same draft (so both can't go #1)

1. Larry Bird was picked a year before Magic, before he declared, otherwise they go #1 and 2. Picking a year earlier than declared is no longer allowed in the NBA due to Auerbach taking Bird.
2. Moses Malone and Erving both would have been #1s if not for the ABA
3. Jordan was same year as Hakeem, so both can't both be #1
4. Wade was same year as Lebron, so both can't both be #1 (and technically, Shaq was a #1 for that team)

The Spurs actually had three #1 picks in their first championship.
Pistons had the #1 and #2 picks in the same draft. (Aguirre and Thomas)
Lakers with Magic and Jabbar had two #1 picks. And McAdoo was a #2

 

I think Melo counts, too, via the same draft exception.

 

The exceptions are simple. If the #1 in a class who has a title does not win a championship, the #2 in the same class does, that's the Magic/Bird exception and Hakeem/Jordan. And this is offset by how many #1s where on championship teams. Like I said, Spurs had three Top picks in their first title. Lakers had two in all five of Magics. Pistons had Aguirre and Thomas #1 and #2 in same draft for two chips.

All your imagination has to do is accept MJ and Hakeem were top two 84. If Rockets don't take Hakeem #1, we damn sure were taking Jordan. That's just fact. Forget about what Portland did. That's 8 rings

Bird and Magic are an exception, No? With NBA rules now, Auerbach cannot draft Bird in 1978 at 6th. He has to wait for Bird to declare. Auerbach took Bird the year before he came out in the draft? So, with rules now, Bird goes in the same draft as Magic. How can they both be #1s in 1979. We all know they would have been 1 and 2. That's 8 rings.

The next exception is the ABA. Erving was clearly going to be a #1. He averaged 20ppg and 20rpg in his final college year, but he signed a $1m contract with the ABA, so he fell to #3 in the draft. He was still #3 AFTER signing an ABA contract. Likewise, Moses Malone signed with the ABA and was a clear #1.

If Lebron's not in the '04 draft, there is no way Cleveland takes Darko...But we can add Wade to the teams without a #1. I'm fine with that. So six teams, except for the fact they had Shaq

That's it. That's all the exceptions. The Bird Rule and the ABA.