The non-stop running is almost never the pump itself failing - it's a symptom of something else happening in your basement. That said, there's one thing the other answers didn't emphasize enough: check your float switch first. If it's stuck or the mechanism is jammed, the pump won't shut off even when the water level drops. Give it a gentle wiggle and make sure it moves freely. Sometimes debris or mineral buildup causes this, and it's a quick fix.
After that, yeah, look at what's bringing water in. New cracks in your foundation or walls, gaps where pipes enter, a blocked or failing floor drain, even a sump pit that's too small for your current water table - any of these could be the real problem. But here's the thing: if you haven't had rain and the pump's still hammering, you might also have a plumbing leak somewhere above the basement floor. Check under sinks, around your water heater, anywhere there's a supply line. A slow leak can pump out a ton of water over days without you noticing it.
Before spending money on a replacement pump, pull the cover off the pit if you can and inspect it. Is the water level actually rising? How dirty is the water - clear or full of sediment? That tells you a lot about whether you're dealing with groundwater, a broken pipe, or a foundation issue. What does the pit look like when the pump's running versus when it shuts off?