when is a message queue overkill, like prob too much for some stuff

So, I've been chewing on message queues recently, especially when they seem to create more headaches than they fix. People always suggest them for splitting up services or doing background stuff, right? But when does it make more sense to just call an API directly, or maybe use a shared database instead? I'm wondering if there are certain situations or sizes of projects where you'd absolutely go with a queue, and others where you'd say, 'nah, let's skip it.' I'd love to hear what's worked for you and what the downsides were.