Depends on what you class as a "dungeon". I don't think this will be a traditional Zelda title, so it's tough to tell.

However, more than 10 for sure.

I would class it as a puzzle filled enclosed area which contains a compass, a map, a new item, a boss key and a boss for which you recieve a full heart piece upon defeating. Those are my requirements.

Hopefully not less than 9. Ideally 11.

Hopefully 10 maybe 9 or 8 but not less

I would take 5, but I want great and large dungeons compared to the past. Also want a final dungeon (duh), a multitude of explorable caves (mini dungeons, dont actually have to be caves. A forest for example could be turned into a mini dungeon) and a massive expert dungeon (of course optional to finishing the game).

I think that there will be 7 main dungeons. They will be bigger, and more unique than the dungeons we have previously seen.

On top of that there will be many caves/mini dungeons spread out throughout the game that are optional.
This is mere speculation, obviously.

OOT had 9 main dungeons, really, not 10. Inside the Deku Tree, Dodongo's Cavern, Inside Jabu Jabu's Belly, Forest, Fire, Water, Shadow, and Spirit Temples, and Ganon's Tower. 12 if you count the Bottom of the Well, Ice Cavern, and Gerudo Training Grounds mini dungeons, which Zelda Dungeon does, so seems legit to me. I'm personally hoping for 8-11 main dungeons and several mini dungeons, maybe even more than main dungeons. I recall them saying in interviews that every idea that anyone on the team comes up with can be put in due to the size of the game, so dungeon concepts that wouldn't make for full dungeons can become mini dungeons. So I'm not getting my hopes up but I could totally see 20+ dungeons when counting mini dungeons. There's definitely room for them, be they big as OOT Hyrule Field or not. Zelda U Field looks like you could fit about 16 OOT Hyrule Fields in it. So figure 9 OOT field sized dungeons, plus about 12 mini dungeons a quarter the size of that, many entirely underground as well, and you'd have plenty of room for them with tons of extra room for towns, castles, bridges, and rolling hills, plains, rivers and mountains. Don't get overhyped though, as we could be overestimating what the team has time to do. The game has undergone huge revisions, after all.

It all depends on what you define as a dungeon what the nature of the side quests will entail. If you only consider a dungeon something where you get a new item/and or pertains to the main story(gannon's fortress or something along those lines), then I would say around 8. Now if you're like me and you consider a dungeon maybe something shorter that takes all of 5 minutes or so(think Skyrims random caves a.k.a. Caverim) then it could have well over 50. 

I actually hope they bring back that pit of 100 trials rip off from Twilight princess!

I dont want too many traditional big Zelda dungeon, but I would love mini dungeons and caves.