Are they all listed as "active" connections, or are some timed out or expired?
That's not a totally whacky #, especially if some/most of them are timed out or closed.
Making sure you have the router firewall on, and that you're not running any P2P stuff like bit torrent or skype running would be smart.
Also on Macs you can go to activity manager and on Win you can go to task manager to look at open background processes and make sure nothing unexpected is running.
If you use Chrome browser it has a really handy live connection monitor under *correction, it's under "chrome://net-internals" then looking at the various pages where you can determine a lot about the places chrome has reached out and touched (obviously only reveals what your browser activity is doing, but it can still be somewhat surprising the # of open connections that web browsing runs through). Also if you want to set your DNS to OpenDNS for a day (Free) and use a local client, or DNS-O-Matic to update it with your IP, you can get very detailed info about all the DNS lookups your network has done.