Your problem is the fact that you're only looking at KEYDOWN events.

What you need to do is toggle a boolean value when a key is pressed or released.

Something like this would work:

# event loop
for event in pygame.event.get():
    if event.type == pygame.QUIT: 
        sys.exit()        
    elif event.type == pygame.KEYDOWN:          # check for key presses          
        if event.key == pygame.K_LEFT:        # left arrow turns left
            pressed_left = True
        elif event.key == pygame.K_RIGHT:     # right arrow turns right
            pressed_right = True
        elif event.key == pygame.K_UP:        # up arrow goes up
            pressed_up = True
        elif event.key == pygame.K_DOWN:     # down arrow goes down
            pressed_down = True
    elif event.type == pygame.KEYUP:            # check for key releases
        if event.key == pygame.K_LEFT:        # left arrow turns left
            pressed_left = False
        elif event.key == pygame.K_RIGHT:     # right arrow turns right
            pressed_right = False
        elif event.key == pygame.K_UP:        # up arrow goes up
            pressed_up = False
        elif event.key == pygame.K_DOWN:     # down arrow goes down
            pressed_down = False
# Now check for key states:
if pressed_left:
    x -= x_speed
if pressed_right:
    x += x_speed
if pressed_up:
    y -= y_speed
if pressed_down:
    y += y_speed

This way, you're actually looking at both presses and releases, and moving while the key is pressed.

Your problem is the fact that you're only looking at KEYDOWN events.

What you need to do is toggle a boolean value when a key is pressed or released.

Something like this would work:

# event loop
for event in pygame.event.get():
    if event.type == pygame.QUIT: 
        sys.exit()        
    elif event.type == pygame.KEYDOWN:          # check for key presses          
        if event.key == pygame.K_LEFT:        # left arrow turns left
            pressed_left = True
        elif event.key == pygame.K_RIGHT:     # right arrow turns right
            pressed_right = True
        elif event.key == pygame.K_UP:        # up arrow goes up
            pressed_up = True
        elif event.key == pygame.K_DOWN:     # down arrow goes down
            pressed_down = True
    elif event.type == pygame.KEYUP:            # check for key releases
        if event.key == pygame.K_LEFT:        # left arrow turns left
            pressed_left = False
        elif event.key == pygame.K_RIGHT:     # right arrow turns right
            pressed_right = False
        elif event.key == pygame.K_UP:        # up arrow goes up
            pressed_up = False
        elif event.key == pygame.K_DOWN:     # down arrow goes down
            pressed_down = False 

# In your game loop, check for key states:
if pressed_left:
    x -= x_speed
if pressed_right:
    x += x_speed
if pressed_up:
    y -= y_speed
if pressed_down:
    y += y_speed

This way, you're actually looking at both presses and releases, and moving while the key is pressed.