Although the Hyrule in Breath of the Wild is much changed, you can find the ruins of some familiar locations. Once such location is the Lon Lon Ranch from Ocarina of Time. In these ruins, you can find structures that match the layout of the ranch.
Inside the Sanctum, you can spot a symbol that matches the Gate of Time from Skyward Sword. Check out the video below for a comparison.
Several songs from past Zelda games have been hidden in the music of Breath of the Wild songs at different speeds. These include:
There is an NPC named Botrick who bears a strong resemblance to Satoru Iwata, the president of Nintendo who died in 2015. Not only does he have a similar appearance, but Botrick also talks about Satori Mountain and the Lord of the Mountain who appears there.
If you climb to the grove in Satori Mountain, you can find the Lord of the Mountain and take a picture of it with your Camera Rune. This adds a note to the Hyrule Compendium that states the Lord of the Mountain is believed to be the reincarnation of a sage named Satori.
The runes that appear on the Sheikah Slate and in Shrines are based on the Hylian text from past games in the series, which has let fans translate the messages found in the game. Some are serious, but some are humorous, including one that reads “All your base” in reference to the infamous “All your base are belong to us” line from Zero Wing.
As has become standard in Zelda games, attacking a Cucco enough times makes an entire flock of them attack you.