Here are 4 websites that require no registration for sending SMS on mobile:

SMSTI.IN - Smsti.in allows you send message of complete 160 words and without any ads.

SEASMS.COM - Seasms allows you to send messages all over the world.

SPICESMS.COM - Spicesms allows you to send sms only in India with 130 character support for sms.

BOLLYWOODMOTION.COM - Bollywoodmotion is one of the best sms website as you can send sms upto 500 characters long.