A misspelled or otherwise botched link will also be red, even if the page it was intended to go to does exist.
Some links are Frequent Redlinks, such as misspellings and abbreviations, that should be changed.
Links to works that don't yet have pages will also show up as red. However, they'll automatically shift to blue when the page is created, so don't be afraid to link to works this way--it makes it easier for when someone eventually writes it up.
Not to be confused with the red Link from The Legend of Zelda Four Swords, The Legend of Zelda Four Swords Adventures, and Super Smash Bros., nor when he's wearing a Red Ring, the Red Mail, or the Goron Tunic.