Hi Carl,
This is always tough for a ecommerce site. I have heard some people say dont worry about it, others say you should always be around 100. But if we use amazon.com as an example they have about 300+ links on any given page, yes they are Amazon and a content giant but it tells you too many links on a page isnt the end of the world.
If I was you I would concentrate more on great product descriptions/content than keeping the links down.
I am counting 175 links on your homepage.
If you really want to get that number down a bit, here are some observations I noticed at first glance:
You have 17 links in your footer - all of which seem to be useless, start by getting rid of those.
It looks like there are multiple items in the dropdown menu also what could be duplicates (you have maternity under dresses, but you also have dresses under maternity). See if you cant combine some links and shorten up your dropdown menus also.
I think you can easily trim your links down you just have to be creative, but those should give you a starting point.