Which placed items give free buffs?

Solution 1:

Auras

Star in a bottle gives increased mana regeneration.

Heart Lantern gives increased health regeneration (and stacks with fire)

Dryad increases your defense, you can build a house near your arena and then move her into it

Sunflower's increase movement speed (and decrease monster spawn rate)

Honey improves health regeneration (while or after standing in it) however it will also slow you down so use wisely

Enemy Banners Provide increased damage to and reduced damage from a particular enemy.

Activates

Bewitching Table allows you to summon another minion

Ammo Box - 20% chance to not consume ammo

Sharpening Station increases armor penetration of melee weapons

Crystal ball increases magic power

Misc

Using Asphalt as the floor will give you an acceleration as well as movement speed bonus

Heart Statues connected to pressure plates can give you a quick small boost to your health every now and then

Star Statues similarly give you a small amount of mana

Solution 2:

Expanding Aequitas's answer there's also:

• Garden Gnome: Increases Luck, effectively increasing damage inflicted and reducing received.
• Bast Statue: Increases defense by 5.