Can only agree with others here, just links do not create queries. By looking at your index page I see 47 queries used. thats a little over normal, but not unusual since you are using among other things, random gallery images. Some other blocks as well might create more connections. But its not really extreme or anything, since you don't have too many visitors at any time either.
One thing that can contribute to it, is if you are using any mysql calls that DON'T use db_query..as that is NOT calculated into that info down on the page. It may then be quite a few extra..and certainly way too much. But again, for example simple webshop scripts use up to 70-100 connections on a page load, so its really a sign of the need to move to another host imho.