Among those pairs are those for the verbs "to ask," "to leave," "to apply," "to have," "to play" and "to take." This list is by no means exhaustive, but if you can learn how to properly translate these verbs into Spanish you will be well on your way to avoiding some of the most common verb-choice mistakes made by non-native speakers.
To ask: pedir and preguntar
If you're making a request for a thing or some action, use pedir. But if you're asking for information about something, use preguntar. Remember that pedir can be translated as "ask for" or "request," so you don't need to follow it with a preposition. Me pidió tres dólares, he asked me for $3. Me preguntó por tres dólares, he asked me about the $3 (as what happened to it). Me pidió que cocinara la comida, she asked me to cook the meal. Preguntó si había cocinado la comida, she asked me if I had cooked the meal. Note that pedir is irregular.
To leave: salir and dejar
If you're leaving in the sense of exiting or going away, use salir (you may remember that "an exit" in Spanish is una salida). But if you're leaving an object somewhere, use dejar. El tren sale a las ocho, the train leaves at 8. Dejé mis libros en el tren, I left my books in the train. Dejar also can mean "to leave" in the less common sense of "to allow." ¡Déjame salir! Leave me go! Note that salir is irregular.
To apply: aplicar and solicitar
If you're applying in the sense of applying for a job, use solicitar. If you're applying something, use aplicar. Tres personas solicitan el puesto de redactor, three people are seeking the editor's position. Tengo que aplicar el bronceador, I need to apply the suntan lotion. Note that aplicar is irregular. You also can use aplicarse for "to apply oneself." Mi hijo se aplica mucho en sus tareas escolares, my son applies himself well to his homework.
To have: tener and haber
"To have" in the sense of "to possess" is tener. Haber is usually used much as the English "to have" as an auxiliary verb with the past participle. Tengo tres libros, I have three books. He leído tres libros, I have read three books. That difference is straightforward. But both verbs can also be used with que to indicate necessity. Tener que followed by an infinitive means "to have to," while hay que (hay is a form of haber) also expresses necessity but doesn't specify who is performing the action. Tengo que leer tres libros, I have to read three books. Hay que leer tres libros, three books have to be read (or, it is necessary to read three books). Both tener and haber are irregular.
To play: jugar and tocar
Use jugar when talking about playing a game, tocar when playing a musical instrument. Me gusta jugar al béisbol, I like playing baseball. No me gusta tocar el piano, I don't like playing the piano. Both jugar and tocar are irregular.
To take: llevar, tomar and sacar
Use llevar for "to take" in the sense of "to carry" or "to transport." But use tomar for "to take" in the sense of "to take for one's use." Use sacar for "take out" in the sense of "remove." Me llevas al aeropuerto, you're taking me to the airport. Tomo el tren al aeropuerto, I'm taking the train to the airport. Tengo que tomar la medicina, I have to take the medicine. El dentista sacó las muelas, the dentist took out the teeth. Sacar is irregular.