Let us change view points.
I am the world government, and I believe this to be a list of your offenses.
1. Association to Red Hair Shanks. Shanks is considered one of the four most dangerous pirates on the Grand Line. Strawhat Luffy is seen as a disciple to a yonkou, and just be association alone, is a wanted man for more information on Red Hair.
2. The Strawhats are flying a pirate flag. Anywhere they go, fear would most likely be the first reaction.
3. Strawhat Luffy infiltrated and disrupted a marine base (Morgan); he also played a key role in the escape of a prisoner (Roronoa Zoro.)
4. Roronoa Zoro, an escaped criminal, resides on the Strawhats ship.
5. Strawhat Luffy defeated the strongest criminals in East Blue, an obvious attempt to seize control of a sea. There could be possibly no other motive.
6. The Strawhats had the power to enter the Grand Line, and the audacity to fly a Pirate flag; a direct knock at the world government.
7. They supported a rebellion (Drum Island) and helped the rebels thwart a King from reclaiming a kingdom that was part of the World Government.
8. Commodore Smoker has confirmed that Monkey D. Luffy is the brother to Portugas D. Ace, captain of the second division of the White Beard Pirates, another Yonkou.
8. They beat down Shichibukai Pirate, Crocodile. This confirmed their strength and showed their defiance at the World Government.
9. They acquired Nico Robin, a devil that received a 79 million beri bounty at the age of 8. Nico Robin is wanted for illegal activity and possessing the power to restore a power great enough to topple the balance of the entire world.
10. They attacked and destroyed Enies Lobbies, and in the process, defeated Cipher Pol 9, one that was widely accepted as the strongest CP9 ever; headed by Rob Lucchi. Furthermore, they survived the Buster Call, a national level power.
11. Recent information has revealed that Strawhat Luffy is the son to the world's most wanted man: Dragon. Furthermore, Luffy's grand father is Marine Vice Admiral Monkey D. Garp. The lineage of the family is obviously abnormal.
That is a good summary of why the Strawhats are criminals. ;) I'll edit this a bit later, time to go.