It really depends on the license your assets came with.  Some licenses (such as CC0) allow you to do whatever you like.  Others (CC BY for example) might require you to give credit to the creator of the work you've used.  Others let you do what you want, but you have to give credit and share your own work under the same license (CC-BY-SA), or forbid commercial use (CC BY-NC) or all sorts of other stipulations.  All of the examples I used here are Creative Commons licenses.  There are many other types of licenses, I just picked these examples because they are easy to find and relatively easy to understand as examples.

So, the correct answer is "it depends".  What license were the assets you used provided with?

4 minutes ago, lawnjelly said:

And be aware that a lot of assets marked as 'personal use' are stolen assets, that the uploader has no rights to distribute. (The implication being that if you are just using them personally and not distributing, the original owners won't find out)

It amazes me how much is stolen on sites that sell 3D models... Thankfully I don't buy assets from such hubs, only through channels I know and trust if I don't do it in house or myself personally.

If in doubt, use a large site like turbosquid, and pay something for the models.

They have some very expensive models on there, but also some very good ones for pocket change.

Most of my 3D models in my game come from there and/or are kitbashes of stuff on there. Because you've paid them, and they've certified and guaranteed that the license is correct, so long as you abide by the reasonable terms (e.g. don't go using a porsche in your racing game or an AK-47 in your first person shooter!) if someone did try to sue you, you have reasonable defence that you bought it from turbosquid, and paid for it, and turbosquid have done their due diligence, which pins the fault clearly on the asset's seller.

It's not completely watertight and I am no lawyer, but this is how i see it, and it's common sense to me. I'm sure if someone was vindictive enough, they could go after you, turbosquid, and the seller of the asset together.

If in doubt, take legal advice, if still in doubt don't do it!