Picking one of the more common addresses at random (I chose
188.8.131.52) and putting it into a web browser appears to go straight to Google so I would have to say that the
72.14.204.XXX address range is pointing at Google and is most likely a result of the Google+ integration that is becoming more prevalent in every web page you visit. It seems that google want to keep a close eye on what you do these days and so their connections are ongoing rather than fleeting...
That pretty much rules out about 2/3rds of your list, after that the number of connections looks normal for a web browser just generally "doing it's thing"
If you're curious then there is a neat tool Whois by IP Address which can tell you who onws a particular IP address range.
184.108.40.206 -> Akamai Technologies, Inc (Webapp and download accelerators)
(same for most of the 96.16 - 96.17 range)
Akamai Technologies, Inc. AKAMAI-200710 (NET-96-16-0-0-1) 220.127.116.11 - 18.104.22.168
22.214.171.124 -> Google (again)
Google Inc. GOOGLE (NET-74-125-0-0-1) 126.96.36.199 - 188.8.131.52
184.108.40.206 -> Microsoft (probably Windows Update)
Microsoft Corp MICROSOFT-1BLK (NET-65-52-0-0-1) 220.127.116.11 - 18.104.22.168
Take out those key players and all you are left with is a few general IP addresses for websites and stuff.
While having a bunch of connections like that running is vaguely odd, they are not uncommon these days with always-on internet as most people will not notice them and companies can get away with it.
I very much doubt you have a virus as the large proportion of connections are to reputable companies.