The days after New Year's tend to lead shoppers into a frenzy and the biggest reason has to be due to the Fukubukuro (Happy Bag, Lucky Bag, Msytery Bag etc.) that most stores offer in order to kick off the New Year.
Shoppers everywhere clamor for these bags because these bags contains items that are worth far more than the price you pay for them. The only catch is that you have absolutely no idea what's in them as the bags are sealed. So you may end up getting clothes that don't fit you or are in colours that simply look weird, some stores also put in their past seasons clothes that they couldn't sell off into these bags so there is some risk when you buy them. However, considering that you're probably paying $10 for $100 woth of clothes, shoes and accesories, the value greatly outwieghs the risk and there's always the fun element of surprise in what you get in the bag. Its little wonder that many Japanese girls look forward to the New Year sales and many popular shops and brands often have queues forming hours or even days ahead of opening. Fukubukuro also tend to come in limited quantity, so its important to get into the shops early before they're all gone.
Laforet Harajuku famously starts their fukubukuro sales on Jan 1st, but many other shops including Shibuya 109 start their sales on Jan 2nd. Generally crowds, lots of noise and mayhem tend to occur but not like these will stop any savvy shoppers out there.
Images and information from http://tokyofashion.com/japanese-lucky-bags-2010-lots-of-pictures/