Bike tires are a complex science unto themselves — I've heard people say, "It's not about the bike; it's about the tires." When it comes to filling your bicycle tires, you need to know about the two kinds of valves out there: the tall and skinny Presta valve and the more utilitarian Schrader valve, which you probably had on your first bike way back when.
The Presta valve, sometimes referred to as a French valve, is common on most performance road and mountain bikes — tires that require high air pressure. This style of valve has built-in valve caps, which you open before pumping air into the tire and which must be tightly closed to prevent air from slowly leaking out of the tire. Presta valves are used in high-performance bikes because they are lightweight and slender, so they don't require a large hole in the rim of the wheel, which would decrease the stability of the wheel. Unfortunately, you cannot use the automated air at a gas station with Presta valves without an adapter, which you screw on once the cap has been opened.
The Schrader valve is your basic automotive valve and is generally sturdier. You will find this style used on kids' bikes as well as utility bikes and beach cruisers. The little plastic cap that screws onto the valve is not really necessary for the tire will hold air without it. But the tire may slowly leak, so you might want to check your pressure more regularly. The cap also helps keep debris out of the valve.
What do you have on your bike?