While ink can go bad, it rarely does. Ink is a solution consisting of water, dyes (or pigments), lubricants, surfactants, and biocides. So long as all these parts do their job and stay in suspension, chances are in the ink will be just fine. I have ink from the 1950s that is still very usable.
There are a few warning signs in your ink may have gone bad:
If it appears that a lot of water has evaporated from your ink (i.e., the ink is very thick), the ink may not be great to use in your pens. You can, in theory, add some distilled water back into your ink bottle, but rather than risk it, you may just want to throw it out.
Some inks are prone to growing things like mold or slime. The fountain pen community even has an acronym for it: SitB. (S@#$ in the Bottle.)  If you open your bottle and see mold or slime, throw it out immediately and thoroughly clean any pen that may have recently had that ink.
Ink that has been sitting around for a long time can show some separation of the components of the ink, including sediment on the bottom of the bottle. If there aren't any of the aforementioned nasties growing in your ink, you could probably just shake everything back into suspension, althrough I probably wouldn't do that.
Old inks can exhibit color shifts from their original color or shade. This will especially be true of ink that have been exposed to a lot of light or UV. It shouldn't cause any harm to use that ink, but the color may not be what you were expecting.
If you have an old ink, and everything seems copacetic, try inking it up in a cheap pen. (I keep several around for just such a purpose.) If everything goes well, it should be safe to use!