For me, I can't say that there are hard and fast rules. Some of the factors are size, cost, how often I'd use it, etc...
If the rental costs over the times I'd use it add up to more than the purchase cost of something that is usually a trigger. Especially if I have to figure in the time to go get it and then return it and all. Plus, with eBay there is the option of then selling it again when you really are finished with it. Looking back on it, I wish I had gone that route with the drywall sander. I've rented one maybe three times over the past couple years and the rental cost has been about what I've seen them going on eBay for. Plus, if I had it around I would have likely used if for a couple other smaller jobs instead of doing them by hand.
Size can be an issue. Infrequent use and large size and it can be easier to just rent it than have to store it all the time. Although, I do have a Bobcat that I had always planned on selling again when I was "finished" with it...

I did buy a hardwood flooring nailer. I don't use it all that often, but it doesn't take up too much room in the tool drawer and I've used it for some side jobs that I would not have taken on if I hadn't had it.
Maintenance can be an issue. If I didn't use the Bobcat as frequently as I did, it could be easier to rent one. The one I have is older so that it was affordable, but that means that there is maintenance and repairs to be made...
The other consideration is friends and family with tools. I won't loan my tools out to just anyone. But there are people that I know that have about the same feelings about tools as I do. My father has a pressure washer, rototiller, and certain hand tools I'll likely never buy because I know that I can borrow his. Likewise, there are a list of my tools he borrows when he needs them. My next door neighbor and I are the same way. It definitely expands the "tool inventory" beyond what one person can own or store.
Does that help?