There is no definitive maximum number of links allowed on a page for SEO but there is a rule of thumb. Google has said in the past that 100 links should be the maximum number of links on a page. They did not say they stop following them at that point or that there were other SEO implications. Their reasoning is that a page with more links than that is difficult to use and makes for a bad end user experience.
Another factor that comes into play is Google will only parse up to a limited amount of data before it stops. If you have too many links on your page, Google may stop parsing the page before it gets to quality content and/or content you want indexed.
If you find that a page will have a large number of links on it then you probably set SEO aside and should ask yourself, "is there a better way to do this? Is this the best user experience I can provide"?