7407 are open collector devices, you supply a source voltage, and the 7407 will sink a certain amount of current. That is usually enough for one LED at a time per port. (+Vcc to LED, to 7407, to sink to ground). Power to drive the 7407 is minimal. Remember that with 7406/07/16/17 series, some are inverting(06/16), others are non-inverting(07/17).
If you want to drive/sink more LEDs per signal, you could use buffer devices like ULN2003A (sink) or UDN2981A (source). Those devices can usually source or sink around 125mA per port (8 ports per device) if all ports are on at the same time. With less ports active, one can usually sink/source 400mA per line.
I use a UDN2981A to source (supply power to) of 28V to relays that take between 40-60mA, and I parallel two ports at a time (giving net 4 signal lines out of 8 lines) to give lots of reserve (pulse) power to the relay. These buffer devices can handle higher voltages, like 24V, which can allow things like LEDs to be strung in series to light more than one at the same time.
For other simple LED switching, you can use 2N7000 N-MOSFETs to light LEDs (current sink) up to 60V at 200mA (maximum rating of 2N7000)