You're talking about a couple things here: placeholders, and all the other web controls that I assume you're putting inside these placeholders.
First of all, placeholders themselves are an extremely lightweight control that generate no additional markup and require very little processing by ASP.NET. So you should be able to put hundreds of these on a page while it still being quite fast.
However, the other controls you're putting inside each placeholder have the potential to produce a substantial amount of markup, viewstate, and of course more processing at the server side.
So in fact there is no standard answer for this as it really depends on your particular application and your audience. But there are a couple of things I can share:
1.) Take a look at the final rendered HTML size. Generally speaking I prefer to keep my public-facing HTML pages under 100 KB each and the home page under 20 KB when possible. Obviously it's not the end of the world to make an HTML page larger than this (many popular sites do). But much over this I'd at least consider splitting it up into multiple pages. High speed connections may be common today, but users are as impatient as ever -- so make your site fast. ;)
2.) There's always the question of scalability. To test this you might check out Microsoft's Web Application Stress Tool to try and simulate a peak-load situation. Then take a look at things like CPU, memory, and bandwidth usage to see if it's taking a big toll on the server. Again, if it's too big of a load you may want to consider splitting up the page.