Aside from what @Jeries said (I concur), it would be easier to list the effects that are "must haves" for you.
The Axe Fx III can emulate a LOT of effects... But not everything.
There's very little it can't do... and anyone talking about Strymons and Eventide pedals-- all most of those are are just multi effects just doing preset patches- all of which can be replicated in any Axe Fx, I've said this before- anything a strymon can do a Boss GT-8 or Boss GT-10 could do without the amps/distortion on.
I have owned thousands of pedals... I currently own about 200 today- and I collect them like baseball cards- I don't really use them... I don't really need any of them to get what I need out of guitar/the axe fx/my sound... At a maximum I use a Morley Wah into the front because it's easier at times.
But there's nothing any reasonable person is missing out on. At most, Z-Vex Fuzz Factory and Seek Wah... but I'm sure there's probably some method for it now. I keep a Line 6 M5 and G-Major 2 around for the hell of it... but I don't need anything.