Ok, here's something I just knocked up. I can't guarantee it'll do exactly what you imagined, but I'm pretty sure it'll at least be close. You could also expand it for more LED's (up to 16 using two shift registers) or reduce it down to 8 (one shift register). You could also change how many of the LED's that are 'always 'on', but changing the feedback from to the transistor.
Quick explanation:
The inputs to the shift register at the top, are A and B, these are tied together, although they are AND'd so you could tie A to VCC (+5v) and just have B as the input.
On power up, R3 and C1 make sure that the registers are '0' - so all LED's are off. The 555 timer is configured as astable and provides a 4.8Hz clock to the shift registers. Every low-to-high transition, the shift register takes the input from AB and moves it to the next register, as 'QB' output on the second shift register is 0 (after power up), the input to the transistor is 0, so its collector is at 5V - the input to the first shift register, so this lights up the first LED on the first clock pulse. With each pulse the LED's light up until after 10 pulses, they are all lit - at which point, QB on the second shift register is '1', so the transistor is turned on, pulling the input to the first shift register low. So on the 11'th pulse, the first LED will turn off, then the second, then third etc.. until finally all LED's are off again, at which point the process starts again.
By changing which shift register output goes to the transistor, you can change how many LED's are lit at any given time... so, say you wanted a line of 6 LED's to be lit, moving across the display, then the input to this transistor will be the first shift-register QF.
Just to complete it I've added a regulator circuit.
Note this will only scan the LEDs one way.
Any criticisms welcome, its just a quick 15-minute rough draft. I've kept the resistor and capacitor values mostly the same for convenience (10uF, 10k, 220ohm, 100nF). changing R14 and R15 will change the speed of the clock, so you could replace one of these with a potentiometer for control.