They Are Amazing...

               Their first single Hug reached fourteenth best selling in 2004.

   In the same year, their second single 'The Way u Are' reached ninth best selling record.

    Same year again, Their first album 'Triangel' reached on top chart and got eighth best selling record too.

 Their second album 'Rising Sun' got the Best Music Video and the People`s Choice award at 2005 Mnet

 Korea Music FestivalIn their third Album 'O-Jung Ban Hap', TVXQ received 4 award.
They are Best Artist of The Year, Best Group, Mnet.com, and Mnet Plus Mobile People's Choice Award.They also got Daesang and Bonsang award for their third Album O-Jung Ban Hap.

 For their sixteenth single 'Purple Line', they became teh first foreign male group to have number-one single in Japan.

Their fourth album 'Mirotic' made them to be the first Korean Album in six year.

  'Keep Your Head Down' is in number one (TOP) for TV theme Song Award in Japan, and became a soundtrack for Japan Drama 'My Beautiful Neighbour'.

 JYJ promote the EP The..., was released in September 2010, and debuted at No. 1 on Oricon albums charts. The DVD for their Thanksgiving Live in Dome concert sold 116,000 copies and their album The... sold 140,000 albums in the first week after being released, with both debuting at No. 1 on the Oricon DVD and album charts in the same week. 

 They are recorded as an idol who have the biggest fans in the world by Guiness World Record. Cassiopeia are about 800.000, Biggeast are about 200.000. iCassie and iBiggeast are more than 100.000.

There are a lot of award which they got...

But I just Mention some of them...

Source : Wikipedia