Being able to start your car doesn't mean it's safe to drive, and thinking that you can or should drive it when it's breaking down or acting up can mean putting your safety at risk. A car that shuts down while on the road can mean needing to have it towed anyway, and facing larger repair bills. Note a few signs that tell you that your car should be towed even if you can still turn the key and get it running.
Clicking, battery light
Your engine may turn over but if you hear clicking sounds before it starts, this usually means the battery is wearing down and is not charging the electrical systems in the car. Those systems may start to work but they can fail while you drive, and these systems include pumps and fans that keep your car operating.
The battery light on the dashboard is a similar concern; this light usually means that the battery is not being powered properly. Your car may need a new alternator, which recharges the battery as you drive, or the alternator belt may have snapped. This belt keeps the alternator running and connected to the battery. Whatever the case, if the battery light comes on, you should turn off the car rather than continuing to drive and drain the battery.
Squealing and a snap, thumping
Squealing usually means a belt is coming loose and the snap means the belt has now broken. You may hear a thumping or whirring sound as you drive, as a broken belt thumps around before it falls off. The broken belt may be to the fan that keeps the engine cool or to the alternator, as mentioned above. Driving without these being fully operational can mean quite a bit of damage to your engine and risking the car just shutting down.
If you hear a snap without squealing and then a thumping, this usually means a hose has broken loose or cracked open. Very often you'll see fluid spilling out under your car when this happens. Those hoses deliver fluids to all parts of your car including the engine, power steering, transmission, and the like. Once the fluid leaks out completely, your steering may seize up or the brakes may fail to work, or the car may get stuck in neutral. When you hear a snap of any sort, with or without squealing or thumping, it's good to have your car towed to find the cause and have the belt or hose replaced as needed.