Several factors play into whether you ought to leave your laptop on 24/7, turn it off overnight or put it to : battery use, heat, electricity costs and wear on the system. In most cases, however, the bottom line is: yes, you can leave your laptop on in most situations, except for an occasional reboot.
System Wear and Tear
It's true that leaving a computer on when it is not in use places additional wear on some of its components, most notably the hard drive, which keeps spinning. However, turning your computer off and on frequently also strains the drive motor as it spins up and down. In practice, worries about wear shouldn't play a major part in your decision. Yes, many hard drives list lifespans measured both in hours of runtime and start/stop counts, but these lifespans are so high that you'll most likely replace the computer or have the drive die due to an unrelated problem long before you reach them. In fact, drive manufacturer Seagate no longer uses these "Mean Time Between Failure" lifespan numbers due to how poorly they reflect real world use.
One factor that does play a role in computer failures, both of the hard drive and other components, is the temperature inside the computer. In laptops, temperature is especially troublesome, due to how little airflow they have compared to desktops. Heat presents a second downside in laptops, as constant heat shortens battery lifespan.
If your laptop manages heat well, you can safely leave your computer on overnight, as long as you place it on a hard, flat surface and don't block the vents. But if your laptop often grows too hot to touch, you might be better off putting it to sleep or shutting it down when you aren't around, both for the laptop's well-being and as a precaution against fire or heat damage to your furniture.
While the laptop is plugged in, you don't need to worry about its battery charge, whether the computer is on or off -- lithium-ion rechargeable batteries can't overcharge. Away from home, however, you can't afford to leave a laptop running while not in use, as most laptops last only a few hours on battery. Sleep mode provides a longer-term solution, providing a day or two of life on battery, but for long trips away from the charger, put your computer into or shut it down between uses. Both options completely turn off the computer, but waking a hibernating computer restores your programs right where you left them.
Laptops use little electricity, even compared to desktop computers -- less than 100 watts, and often less than a light bulb. Even so, any amount of electricity costs money, so if you're trying to save, put your laptop to sleep overnight. A sleeping PC uses only a watt or two, and wakes in a matter of seconds.
No matter if you use a laptop or desktop, Windows or Mac, a computer needs to reboot occasionally to install updates, remove a program or escape a freeze. Even if your computer doesn't ask to reboot, try it as a first step when you run into problems -- it fixes more glitches than you might expect.