When is having too many links a bad thing? I'd argue anytime the number of links exceeds the abilities of the user to quickly find their way through your web site or application. There's no magical number. However, if two or more confident clicks are needed rather than one confused and delayed click, I bet you'll have a happier user.

I needed to hit GoDaddy tonight (my web registrar) to check some settings quickly. This web page welcomed me (click for larger version):

# of links: more than 150

Amount of time searching page for "Login": too long

Time taken before realizing "My Account" was the same as "Login": too long

These are the types of web sites that I usually avoid as they're so link heavy, I'd rather try somewhere else first that feels less cluttered and easier to get through. After a certain number of links, I also associate it with a search-engine-link site of some sort and move on as non-trustworthy. If I hadn't already used GoDaddy, I definitely wouldn't be welcomed by their home page and wouldn't come back.