First and foremost, solderless breadboards are rarely a deployable format for electronic circuits. They work pretty well for certain (not all) kinds of prototypes. If you have a circuit that you intend to have any sort of lifetime, your plans should include some way to get your circuit off of a solderless breadboard, and into something more permanent.
There are a number of things you can do to make your life easier.
Things like color codes really help. Pick standard colors for Vss, Vcc, and ground. Stick with them. As mentioned by others, place pin 1's for all IC's in the same orientation. For inportant locations, make a little flag with a stub of wire and some tape to make a label. Sometimes it's useful to populate all your IC's first, and get them all powered and grounded neatly before you implement anything else.
The biggest thing you should do, however, is to break your circuit up into functional subcircuits in your head, and plan in advance how you intend to test whether a subcircuit is working. Then, build it, test it, leave it alone, and move on to the rest of the circuit.
Usually, I do this from left to right -- inputs moving along towards middle stages, moving along toward output stages. That's a generality, however, and sometimes it makes more sense to deal with output stages first -- usually on the right side of the board.
If you're doing microcontroller design, this can get confusing, because the architecture is more of a central hub thing, with one unit receiving and sending ins and outs. In this case, you need to have a microcontroller setup that isolates various subcircuits, one at a time to let you test them. It should generate whatever test signals you need. Be sure to remember some reset circuitry.
Of course, breadboards are not robust. You move an oscilloscope probe, and short a cap to a resistor that's not mounted as stably as it should be. That's just the nature of the beast. When a circuit gets too big and complex, there are diminishing returns to leaving it on a solderless breadboard, mostly because of unintentional stuff like surprise shorts on a circuit that worked 5 minutes ago. Take the time to put down your working subsections on soldered breadboards. Better yet, build and test a subcomponent, plop it into a PCB design, and move on to the next subcomponent. Spend a few dollars and a week to get your prototype PCB, populate it, and enjoy your functional circuit.