Logo history of Google Analytics
Initially it used to be called Urchin Software and was an independent web analytics US-based company that eventually was acquired by Google in March 2005 to bring knowledge needed to build Google Analytics.
Here is how Google Analytics used to be in 2007 (courtesy of Jesper Rønn-Jensen @ JustAddWater):

#Google Analytics in 2007
Urchin as paid software has been offered by Google till March 2012, offering #web analytics services for advanced needs (here is a list of the main differences between GA free and Urchin 6).
In the meantime Google Analytics since its first launch in November 2005 (invitation-only, the public definitive release was not available until middle 2006) has been further developed to reach the current stage where it is offered in two versions: free and paid (Premium).
A little curiosity: despite being dismantled, #Urchin name is still alive in GA cookie UTM, acronym of Urchin Traffic Monitor, and UA that compose GA ID’s and stands for Urchin Analytics (and not for Universal Analytics, the new advanced release still not fully integrated with other Google products though).
Let’s have a look at GA branding during the years. Most of long-term users will certainly remember some if not all of the following logos:
1) Urchin logo before Google acquisition
2) Urchin after Google acquisition (2005)
3) First #logo of Google Analytics
4) Renewed logo of Google Analytics
5) Logo of Google Analytics as seen in February 2014, 9 years after its first appearance in the market
6) Updated GA logo after Google re-#branding
7) The new Google Analytics 360 Suite launched in March 2016 has a new set of logos and here GA, that just became part of the suite, has a new design (no more up and down, just a positive trend this time), keeping the same colour.