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I have a list of requirements for a program, but I don't know what program meets these criteria. That's about general-purpose software, for example, not a programming IDE or statistical workbench, questions about which would certainly go to respective sites.
Is this question appropriate on Stack Overflow? Where should I ask about it? On Super User or elsewhere?
Software Recommendations Stack Exchange is a site that does just that.
Please note that like anywhere else on Stack Exchange, questions like “what's the best …” are not answerable and will be closed. A software recommendation question should both provide precise requirements (what platform it needs to run on, what specific functionality is absolutely needed, etc.) and explain for what purpose the software will be used. Precise requirements avoid getting answers that won't be useful because the software lacks a critical feature. A statement of purpose or user story allows answerers to look for the best fit for the task. You are strongly encouraged to read the question quality guidelines before asking a question on Software Recommendations.
Software Recommendations Stack Exchange accepts questions about general-purpose software, development tools and libraries, as well as more specialized software. However, for more specialized software where only a specialist can answer, you are more likely to get good answers if you post on a specialist site instead (do not post on both sites!), if there is one. Even so you are encouraged to read and follow the Software Recommendations Stack Exchange question quality guidelines.
Games are on-topic only inasmuch the question states a purpose (e.g. educational games); "what games are fun?" is not an objectively answerable question.
Note that hardware (what to run the software on) and hosting (who can run the software for you) are off-topic on Software Recommendations. Hardware recommendations have their own site.
I upvoted the other answer because I agree 100% with all but one point made. My point of divergence is on:
... for more specialized software where only a specialist can answer, you are more likely to get good answers if you post on a specialist site instead (do not post on both sites!), if there is one.
As a moderator on one such specialist site (GIS), my advice to anyone wanting to ask for a GIS software recommendation is to try Software Recommendations first.
For those who still want to ask our GIS specialists using the Main site of GIS SE, my next advice is to not ask for software recommendations directly.
I think you will find that if you:
then you will most likely receive answers that either alleviate that concern, or most professionals, recognizing someone on the "wrong track", will say "you may want to try XXX instead because it meets that requirement in this way".
As soon as you outright ask for a recommendation you are asking for the community to put together a list of options for you to choose one from i.e. most answers will be wasted effort by our volunteers.
Alternatively, such questions can usually be asked freely in a site's main chat room.