In dressage Germany is the favorite for gold, especially after the form their riders shown at the German championships. As in most sports, World rankings are not the best reference. The key of German favoritism are the young horses that are really coming through this year. Werth will ride a younger horse which is actually better than her injured ones. They also have Dorothee Schneider & Showtime and Sonke Rothenberger & Cosmo as the shooting stars with young horses. Sonke is actually the son of Sven Rothenberger, who "deflected" from Germany to Netherlands in the 90s and actually won a couple of Olympic medals for your nation Great Britain should be the second best. Charlotte Dujardin & Valegro dropped from the top of World ranking only because they didn't compete since the Europeans last August. They also have Fiona Bigwood & Orthilia who are going very well lately.
As for Netherlands, I don't see them winning anything more than a bronze, and even that could be a problem. Edward Gal competed only once this year with Undercover, and Undercover was so tense that he almost jumped out of the arena in that competition. A lot of people are saying that the horse lost his confidence in the arena after being eliminated at the Europeans last year. And just this week, it was announced that Gal withdrew from the 1st (out of 2) Dutch selection event. " The KNHS has not disclosed that proving form at just one show can suffice for team selection." There are also some rumors that Diederik van Silfhout's horse is struggling with fitness. So it seems that Dutch team might very well depend on Adelinde Cornelissen & Parzival scores once again. Although it's never good when you have to depend on "grandpa" horse, who is already 19-years old. Considering how well USA (and Sweden) are going this year, I actually wouldn't be surprised if Dutch miss out on the team medal. USA's chances were especially boosted by Kasey Perry-Glass & Dublet, who stunned everyone in their first ever competition in Europe.
In eventing Germany is the favorite, following the tradition of recent years. They should be followed by New Zealand, Great Britain, USA, France and Australia. Saying that, Netherlands has overperformed at some recent championships so maybe they can do it again.
Traditionally, jumping is the least predictable of the three. USA, Germany, France, Netherlands and Great Britain are the big five I guess. American guy McLain Ward is looking very good this year. But we mustn't discount Switzerland, Brazil, Canada and the World selection team called "Ukraine". Yep, Ukraine's new addition to the team is Ulrich Kirchoff, German guy who won both jumping gold medals in Atlanta in 1996... Ukraine is the Azerbaijan of equestrian World, a disgrace. Their team for Rio will likely be made of two Germans, one Brazilian and one Hungarian.