What to check before renting a car for a European trip
Questions to ask your rental company before assuming your vignette is covered.

Picking up a rental car adds a genuine layer of uncertainty to vignette planning, mostly because the answer to 'is it included' isn't consistent across companies or countries. Some agencies bundle a valid vignette into the rental price without you having to think about it. Others hand you the keys and expect you to sort out the vignette yourself. There isn't a general rule that applies everywhere, which is exactly why it's worth asking directly rather than assuming either way.
Ask about the vignette specifically
Don't rely on the rental confirmation email to mention it, because plenty of them don't. A quick question at pickup, or ideally before you arrive, tells you whether you need to buy one yourself and for which countries. If you're planning to cross into a second or third country during the rental, ask about each one individually. A vignette valid in Austria doesn't help you in Switzerland, and a rental company covering one country doesn't necessarily cover the whole route you have planned.
Check the vehicle's weight and class
Vignette pricing and requirements aren't the same across all vehicle types. Standard passenger cars, motorcycles, and anything over 3.5 tonnes are often priced and categorized differently, and a vignette bought for the wrong class won't be valid even if you paid for it correctly otherwise. If you're renting anything larger than a typical car, such as a van or a camper, it's worth confirming which weight class it falls into before buying a vignette for it.
Watch for previous renters' vignettes
With older paper-based systems, a sticker left on the windscreen by a previous renter doesn't automatically apply to you, and driving under the assumption that it does is a common way to end up unvalidated at a checkpoint. E-vignettes solve this specific problem since they're tied to the plate number rather than the vehicle's windscreen, but it's still worth confirming which system the country you're in actually uses.
Keep the paperwork or confirmation accessible
Even with an e-vignette, having your confirmation email or purchase record accessible on your phone is useful if you're ever asked to show proof, particularly at a manned checkpoint rather than an automated camera. It's a small thing, but it turns a potential delay into a non-issue.