According to the International Astronomical Union we have eight major planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune; and five dwarf planets: Ceres, Pluto, Haumea, Makemake and Eris. The IAU left it a bit ambiguous as to whether dwarf planets count as real planets or not. If you count the dwarf planets as planets, then yes, there are indeed thirteen – if you don’t count them, then no, there are only eight.
However, just because the IAU only lists 13 planets doesn’t mean there are only 13. For an object to count as a dwarf planet it must be massive enough for its gravity to pull it into a rounded shape – and most dwarf planets lie very far out in the solar system, in a zone of icy, distant small objects called the Kuiper Belt, so they only appear in our telescopes as points of light. We have confirmed at least 13 objects orbiting our Sun are round, but there may be dozens more. Some astronomers believe there may be as many as a hundred dwarf planets in the Kuiper Belt, so perhaps in the future the choice will be between eight and a hundred rather than eight and thirteen!
If you don’t count dwarf planets, the eight planets in order from the Sun are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune. You can remember them with a mnemonic like My Very Eager Mother Just Served Us Noodles. And you can remember the five dwarfs in their proper order with Counting Planets Here Means Eight.
If you count dwarf planets, then the thirteen planets in order from the Sun are Mercury, Venus, Earth, Mars, Ceres (in the asteroid belt), Jupiter, Saturn, Uranus, Neptune, Pluto (in the Kuiper Belt), Haumea (KB), Makemake (KB) and Eris (KB). You can use this mnemonic: My Very Easy Method Can’t Just Speed Up Naming Planets, However Many Exist!