Q: Are there any types of inventions that can't be patented?

A: Yes. This happens all the time.

For example, if you invent something that already exists or was already published, then you cannot patent it because of 35 USC 102. Or, if you did not invent it, then you cannot patent it either.

Or, if you invent something that is obvious in view of something that already exists or was already published, then you cannot patent it under 35 USC 103.

Or, if you invent something that you did not disclose or you did not describe well enough in your patent application, then you cannot patent it under 35 USC 112.

Or, if you invent something that does not fall within the four statutory categories of invention (i.e., process, machine, manufacture, or composition of matter), such as a mathematical formula, then you cannot patent it under 35 USC 101.

Or, if you invent a tax strategy method, then you cannot patent it under AIA section 14.

There could be other reasons why your invention cannot be patented.

A: The answer from Peter Mlynek is accurate. Here are some additions. If you are interested in seeking the edge of what types of things are excluded under 35 USC Section 101, you may want to look in Wikipedia starting with https://en.wikipedia.org/wiki/Bilski_v._Kappos and https://en.wikipedia.org/wiki/Alice_Corp._v._CLS_Bank_International. The material used to train patent examiners on Section 101 can be found at https://www.uspto.gov/patent/laws-and-regulations/examination-policy/subject-matter-eligibility.

Finally, you may have great invention that would be patentable for all the reasons in the patent code but a US government agency can put it under a secrecy hold and block you from getting the patent issued as they do not want the patent in the public domain as it might be used for military purposes. This does not happen often, but it does happen. Your patent is not denied, just delayed. But that might feel like a denial at the front end.

I hope this helps.

Kevin E Flynn