There are 13 Standing stones on the continent of Skyrim. The Lord, The Lady, The Mage, The Warrior, The Serpent, The Tower, The Lover, The Steed, The Shadow, The Ritual, The Apprentice, The Atronach, and The Thief. Each having a different Bonus. You can only have 1 activated at a time so choose carefully.

The Lord- 50 points of damage resistance and 25% magic resistance.
Located East of Morthal and to the South, southwest of Dawnstar.

The Lady- Regenerate health and stamina 25% faster.
Located North of Falkreath and just South of Ilinalta's Deep.

The Mage- Learn Magic oriented skills 20% faster.
Located on the way to Riverwood.

The Warrior- Learn Combat oriented skills 20% faster.
Located on the way to Riverwood.

The Serpent- This stone allows you to use a 5 second paralysis spell that also does 25 damage once per day.
Located NorthEast of Winterhold.

The Tower- Enables you to unlock any expert or lower locks automatically once per day.
Located West of Winterhold and along the North Coast.

The Lover- This stone helps you to learn all skills 15% faster.
Located East of Markarth and West of Blind Cliff Cave.

The Steed- Gives no speed loss from wearing armor and gives you +100 carry weight.
Located Northwest of Solitude right next to Ironback's Hideout.

The Shadow- Become invisible once a day for 60 seconds.
Located directly South of Riften.

The Ritual- This allows you to re-animate the dead to fight for you once a day.
Located East of Whiterun.

The Apprentice- Recover Magicka 100% faster but makes you 100% weaker to it.
Located Northwest of Morthal and North of Fort Snowhawk.

The Atronach- +50 Magicka and allows you to absorb 50% spells damage, though you recover Magicka 50% slower.
Located in the Hot Spring Area South of Bonestrewn Crest.

The Thief- Learn Stealth oriented skills 20% faster.
Located on the way to Riverwood.