Well, the title (kind of) says it all… I just switched to a standing desk (yay!) The only problem is that I don’t have the space I used to have for a book stand on the right (for program manuals, etc.) The only place to really put it is on the left, which would mean it would be sitting directly on the computer itself. Is this a good idea or not? My cat occasionally jumps up there and is immediately shooed off. Is there a reason why I shouldn’t have any weight on top of the computer for any length of time? (I’m kind of thinking there is, which is why the cat thing happens…) But it’s good to ask. And everyone here is so smart! 
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[li]Desktop? No worries.[/li][li]Laptop? No way![/li][/ul]
The main thing is to not go too nuts with the weight (a couple of books, OK, your stack of barbells probably not.) Just be sure not to block any vents, although vents on the top are uncommon until you get to gaming systems.
What kind of computer and how many books?
In general, the answer is no, it shouldn’t be a problem, desktop computer cases are pretty solid. If you are talking about putting a few books on top of a tower case (standing vertically), that should be fine, as long as there are no vents on top that you are blocking.
If you are talking about a computer that is designed to sit horizontally, you’re still probably fine, but I would check the manual - it likely has a specification for how much weight it can support on that side.
there are book holders on a balanced arms (this mechanism is popular with desk lamps with a hinged arms and springs). you might find at an office supply or office furniture store.
Desktop computer cases are still designed to accommodate people who put 20 lb monitors on top. (Or even heavier. Even in these days of flat panels, they’re not light.)
If desk space is at a premium, my recommendation would be to get the computer under the desk in some way. Heavy-duty velcro can allow you to stick it to the underside of the table, which might be ideal with a standing computer station.
Yay! One book on a stand.
And I like the idea of the bookholder with an arm, but it’ll have to wait a little bit.