Not sure these are all low budget, but some always seemed overlooked or underrated. Some I see as imperfect gems of their time.

PS2

• Just Cause 1
• Mercenaries 1
• Rebel Raiders: Operation Nighthawk
• Spartan: Total Warrior
• Super Trucks Racing
• Tom and Jerry: War of the Whiskers

PS3

• Alice: Madness Returns
• Drakengard 3
• Enslaved: Odyssey to the West
• Far Cry 2
• History Civil War: Secret Missions
• LAIR
• Naughty Bear
• Overlord
• RUSE
• Sacred 2: Fallen Angel
• The Saboteur
• Turning Point: Fall of Liberty
• Untold Legends: Dark Kingdom
• Viking: Battle for Asgard

PSP

• Blood Bowl
• Field Commander
• Untold Legends: Brotherhood of the Blade
• Ys Seven

PS Vita

• Army Corps of Hell
• Deception IV: Blood Ties
• Dungeon Hunter: Alliance
• Ys: Memories of Celceta
• Ys VIII: Lacrimosa of Dana

GameCube

• Godzilla: Destroy All Monsters

Wii

• Excite Truck

Mercenaries 1 on PS2 was also great.