Thanks to the lovely dess for this particular recommendation. Xananeko is a flash-based RPG by Yoshio Toshi (or was it Yoshi Toshii), where you get to beat up monsters and collect gold. Move the cat around by using the arrow keys, and initiate an attack by bumping against any of the creatures. Collect items from slain enemies and buy power-ups like automatic health restore from the shop, simply by pressing the up arrow key.
The HP you’ve lost can be renewed by taking a nap at the inn, though not without a financial cost. This action also saves the game, which can be loaded from the main menu if the game ends abruptly.
The sequel can be found here.