Yes!  You can play PS1 games on the A500 Mini.

 

This stick has all the PS1 strategy games in one place!

 

3D Lemmings

Allied General

Baldies

Battle Stations

Brigandine

Chessmaster 3D

Chessmaster 2

Civilisation 2

Command and Conquer Red Alert

Command and Conquer Retaliation

Command and Conquer

Digimon Card Battle

Hogs Of War

Kagero - Deception 2

Lemmings and Oh No More Lemmings

Magic the Gathering

Monster Seed

Panzer Front

Populous the Beginning

Railroad Tycoon 2

Risk

Sheep

Sim City 2000

Syndicate Wars

Theme Hospital

Theme Park

Theme Park World

Transport Tycoon

Trap Runner

Unholy War

Warcraft 2

Warhammer Dark Omen

Warhammer Shadow of Horned Rat

Warzone 2100

Worms

Worms Armadeddon

Worms World Party

X-Com Enemy Unknown

X-Com Terror From Deep