From Ecuador
If you are accessing Peru by land from Ecuador, there are Transporte Cifa has busses leaving from such cities as Guayaquil, Loja, and Cuenca heading south to the border towns Huaquillas in Ecuador and Tumbes in Peru. There is also Macará, a little further inland. Your bus will stop at the migration office, where you will be expected to show your passport, tourist visa, and, perhaps, some proof of financial independence. Resist "help" from anybody who is not an official public servant.
From Colombia
The U.S. State Department warns that "the entire Peru/Colombia border" is highly dangerous due to narcotics trafficking and armed guerillas.
From Brazil
Land travel between Brazil and Peru has been very sparse due to the limited and poor quality roads. There are, however, plans underway to construct major roads connecting Sao Paolo to Lima, and Iberia in Brazil to Puerto Maldonado in Peru. In the latter region there already is a (muddy) road going to the Brazilian border, which you can access via a few min-busses and trucks, but most people prefer to be ferried by boat.
From Bolivia
The most common entry point into Peru from Bolivia is the road heading west from La Paz, which will take you to the border towns of Guaqui and Desaguadero. Some travelers will also depart via boat from the Bolivian coastal town of Puerta Costa on Lake Titicaca to Copacabana, and from there enter Peru.
From Chile
There are busses, trains, and taxis that will take you along the Coastal Highway to the Peruvian border town of Tacna.