About 100-105 with my primary character. (Male Argonian)
Plus a number of texture replacers.
Among them are Francesco's, Natural Environments, Illumination Within, Beautiful Companion, Kobu's Character Advancement System, Cats and Rats, University Cosmetics, Parallax Cities, Bobos Summoned Chest, Darker Dungeons, and a couple of fixes and beta mods of mine own.
I think it should be known that I've hardly had any conflict issues even with this many mods running. However, I did spend time with OBMM making sure the order they were activating minimized conflict issues and I'm also willing to accept the consequences if they do crop up, since the game is hardly worth playing without significant modding. (And definitely worth it, when it is modded so.)
Most of the problems I've had relate to mods battling over which textures to use. (Original, Texture replacer, New mod texture, conflicting mod texture, or none at all.) I've had my eyes disappear once and then more recently, I had the sky disappear during daytime. Both cases were archive invalidation issues, the former using archiveinvalidation.txt, the second using OBMMs method of modifying the BSAs.
As far as other issues... Nothing Gamebreaking, certainly. I once had two buildings dropped in the same place by different mods, but thats the only one I can think of that forced me to choose among them. I also ended up with an unremovable quest item from one mod after grabbing a duplicate from the inventory of a companion produced by the 'unique companions' mod. It took a bit to fix that with the console, but I finally got rid of it.
Alas, I admittedly haven't taken advantage of some of the mods I have installed. The Amnesia Stone, for example, is nice for hiding those annoying quest items that build up in your inventory, but since the Keychain from another mod is a quest item, I have to ditch the stone everytime I want to fiddle with my keys. That or just leave the keys off the keychain constantly, which begs the question why I have the keychain at all. The Skingrad House Basement addon is certainly worth having - well, assuming you have the house, and in my primary game I have been spending more money on spells, furnishing my other homes from the Imperial Furniture mod, and equipping my companion, and getting less money since I hardly find much in the way of expensive weapons as a result of using Francesco's. As a result, I have not purchased half the houses available, including the Skingrad house. Perhaps I will someday, at which point I will certainly enjoy the larger basement provided by the extra mod.
Regardless of the issues, I've had far more fun since installing the additional mods and recommend a bit more adventurous modding of your own games if you really want to enjoy it to the fullest.
Just be ready to pull out the console, spend some time fiddling, or write a small mod to fix the damages if you're unfortunate enough that they do occur.