It will depend on the brand and type. Most should have an expiry date, and should be rated for how long they will last once they've been opened.
Coincidentally I went to develop a film yesterday with Ilford Ilfosol 3 and it had gone bad. I could tell with mine because it's supposed to be clear and yellowish in colour. Mine had turned to a dark brown colour, so it was clear it was gone. Ilfosol 3 is rated for 6 months after opening provided it is kept in an airtight container. You can get collapsible bottles so you can store chemicals without having any air in the container.
With my Ilfosol, I discovered that the seal in the cardboard in the lid hadn't been made, so air had been able to get into the bottle.