This is a good question... I'll give it a go but I'm more than open to correction. I'm basing this solely on ATP so I'm ignoring the Williams sisters' controversy at IW for example.
1. Indian Wells - The first one of the year and so always receives a good degree of attention, it has exceptionally high prize money. The facilities are not far off GS level and nearly all the top players always compete.
2. Cincinnati - This may be subconscious bias on my part as a Federer fan but I think its court speed is fairly unique, very different from IW/Miami etc. On top of this it is one of the oldest tournaments on the tour (founded 1899) and virtually every big name in history has won there, excusing Djokovic (unlucky) and Borg (no surprises on HC).
3. Rome - Again, one of the older tournaments, for me its the biggest clay masters, it also reflects just how good Nadal is on clay, he's won there 7 times and its probably one of his weaker clay tournaments.
4. Paris - Later on in the season, has a different feel to it and it is the defender of the far too undervalued indoor season, a good precursor to the WTF.
5. Rogers Cup - Another tournament I have a soft spot for, It's a shame Federer has not had more success there over time. However, by following Wimbledon it does not always receive great attention and I always feel like the deep runners at Wimbledon spend this time recovering. Also, this event always gets caned during Olympic years.
6. Madrid - Quite a new tournament, still needs to build prestige a bit, like Shanghai below. Again, another reflection of how good Nadal is on clay.
7. Shanghai- This ranks lowly because it is fairly new, hasn't really built up much prestige as of yet. However, by being the only Asian Masters event, holding good facilities and strong prize money it ranks above MC and Miami.
8. Monte Carlo - Despite Federer having never won here I actually really like Monte Carlo. However, it ranks lowly here because it is only optional, rarely gets a full turn-out and is just another addition to an already over-loaded clay season. It ranks above Miami predominantly because of its age and tradition.
9. Miami - This seems a strange pick to be last given that it is part of the "sunshine double", has generous prize money and a big draw. However, I feel it is so close to clay season that many players do not fully take it seriously, turn-out can be poorer and it feels quite samey after IW, not to mention following it closely, so it can be overshadowed.
Good post, which i generally agree with. If MC was still mandatory it would be far higher, probably around 2-4. Now it's just like a glorified 500..
Also, IW facilities are certainly better than the FO or Wimbledon.