Light switches are fine, but for something like a closet or pantry, having the lights automatically turn on and off is really convenient. Here are several ways you can add automatic lights to your closets, pantries, and other areas where you only need a small amount of temporary light.
If There's a Light Socket In Your Closet
If your closet already has a light socket installed, then your options are much more plentiful and it'll be a lot easier to add automatic lights.
If you have a smart home platform set up, like SmartThings and Philips Hue, you can use a motion sensor or an open/close sensor and connect it to a Philips Hue light bulb that you place in the closet. Plus, with a setup like this, you can see when the closet was accessed in the SmartThings app, which is a bit of bonus if that's something you'd care about.
You can also just get Philips' own Hue Motion Sensor and stick it in the closet. It's a lot easier to set up and there are way more settings that you can play around with.
Of course, if you don't already have these products in your house, it can be a lot of money to spend on something so basic. Thankfully, that's not your only option.
Perhaps the easiest and cheapest way is to get a motion detecting light socket adapter like this one from GE ($16). You screw it into the light socket and then screw any light bulb into the adapter. From there, make sure to keep the light switch turned on, and whenever motion is detected, the light will kick on. You can even adjust settings to set how long the light stays on for after it stops detecting motion.
If you have a light switch rather than a pull string, you can replace it with this $20 Lutron motion sensor switch. This will likely only work if the switch is inside of the closet, since it can trigger just by walking past it if it's on the outside, but you can also just stick with a light socket adapter and keep the switch flipped on at all times.
If There Aren't Any Lights In Your Closet
If there's not already a light socket of some kind in your closet, it gets a bit more difficult to set up automatic lights, since you have to figure out a way to get light in there in the first place. Luckily, there are several options you can consider.
The easiest solution is to get some stick-on motion-sensing lights like these ones from OXYLED ($10), which can be attached just about anywhere. You might need a couple of them, depending on the size of your closet or pantry, and you'd have to replace the batteries in them every so often, but it's a cheap and easy way to get motion lights into a space where there wasn't any light previously.
Perhaps a better--but more difficult--solution is to just install a light socket in the closet if it doesn't already have one, or even install track lights. Of course, something like this should probably be left to a professional electrician, but if you already have some electrical know-how and feel comfortable doing it, it's not too difficult a job.
In the end, there are pros and cons to each solution, but depending on your closet layout and what kind of light you need, one solution may be better suited than another.