I have seen many people advocating for Mask of Madness on Juggernaut saying that it helps the ultimate.
Since the ultimate attacks are not considered the same than normal attacks (the damage is not the same than your right click), I am not too sure I understand why this would be true.
http://www.playdota.com/forums/showpost.php?p=1595939&postcount=7
Basically you attack in-between the jumps he makes. MoM would help you get many attacks since it's the cheapest item in therms of attackspeed per gold.
But I'd advice against it. Most things work in public games but MoM is overall not a preferable item since it makes you more squishy, on an already quite squishy hero that's not very good. The build suggested in the link is good though, good balance between survivability and raw damage. Just go phase+aghs first, it's very helpful.
MrSnowman is right. Say a lvl 11 Jugg, your ultimate is consist of 6 ultimate attackts and about 4 normal attacts (this depends on your attack speed). If you have a Mask of Madness, there would be about 2 more normal attackts. See link below. http://dota.tgbus.com/UploadFiles_9207/201005/20100512144820296.jpg
But here I also don't think MoM is a good choice. Mask of Madness is not for late game and in early game, 2 more normal attackts is not worth that money. Aghanim's Scepter, Battle Fury or even Shadow Blade are better than MoM in most cases.
The other answers are currently suffering from being a mite out of date. Currently (especially during the 6.83 patch), Mask of Madness on Juggernaut was the done thing so much it was rare to see a game without it.
The reduction to his base attack time worked well with it, alongside his ultimate, where he got extra auto-attacks while using it.
A solid go to starting build is Boots -> Ring of Aquila -> Mask of Madness -> Phase boots. This is as of patch 6.83 though, so your mileage may vary, depending on the current meta.
