The Arsenal crest has went through quite a number of changes since it came into existence in 1888, two years after the team was first formed, and it is different than the variety of shirt badges that we see worn by the players.

via Arsenal.com
The crest started life based on the coat of arms of the Borough of Woolwich, where Arsenal first started and the three ‘columns’ that could be chimneys are actually cannons.
After a period during and following the first world war, Arsenal wore no crest, but at the start of the 1922/23 season, a new one was unveiled, keeping the cannon that was associated with the club’s roots despite the move to Highbury from Woolwich.
This crest was tweaked in 1925 and the design below would remain for the next 24 years with only minor changes, such as the removal of the text:
via Arsenal.com
1949 saw the club move to a crest that will be familiar to most fans today along with the introduction of the club’s motto, Victoria Concordia Crescit – Victory grows out of harmony.
via Arsenal.com
Just two seasons later, it was tweaked again with the addition of the word ‘Arsenal’
via Arsenal.com
This was the Arsenal crest until the 2001 season when it was ‘cleaned up’
In 2002 Arsenal moved to the crest we see on everything today.
The reasons for this were mostly due to the inability of the club to control copyright on the older images. The club also added about the change, “it had always been one of the Club’s primary objectives to embrace the future and move forward. With Emirates Stadium on the horizon and the Gunners consistently challenging for domestic and European honours, the Club believed it was the ideal time to introduce a new crest” but this is certainly less of a motivating factor than the need to own and control the copyright for commercial reasons.
via Arsenal.com
This crest has changed only once – for the 125th Anniversary of the club in 2011/12