I know that a magician may have a number of Watchers up to his Charisma, and independantly a number of conjured elementals or nature spirits depending on his tradition. Do ally spirits and/or bound free spirits count against the total? Are there any limits to the number of allies or bound free spirits?

No, they have their own excessive costs.

You can only have one Familiar ally unless you've completed all Initiation ordeals and your GM allows you to repeat the Familiar ordeal. Other than the Familiar ally, you can have as many allies as Magic points you'd rather invest than sacrifice to Magic Loss (though Bioware is another attractive option... how handy that Pain Editor and Trauma Dampener add up to 1.0 essence).

There are also Great form spirits.

Anyone can bind free spirits, and if you're Awakened it's a handy way to get access to spirits that you can't summon yourself. Each one is a hassle to acquire and a battle of will to maintain. Although they have unlimited Services for you and must obey you until you die (or another Conjuror wrests control if them from you) they'll quite likely accelerate that process if it's to their advantage.

Also, enslaving multiple Free Spirits is likely to get you a lot of unwanted attention by totems, other Free Spirits, dragons, etc.