SEWAGE BACKING UP

This is pretty obvious, but if you're seeing sewage backing up into your drains and/or water isn't draining as fast as it should even after plunging, there's a good chance your septic system is filled to capacity and should be pumped immediately. Obviously nobody wants sewage backing up into their home, but a backup also indicates that your system is at absolute capacity and not just full. This will often lead to serious repairs if not addressed immediately.
POOLING WATER IN YOUR LEACHING FIELD

Generally the most common sign, pooling water indicates that your tank is at or very near capacity. This isn't necessarily limited to your leaching field, but that is the most common place to see pooling water due to a full tank. When sludge and sediment get to levels that they start clogging drain field pipes, liquid cannot drain properly and starts to gather and rise to the surface of your leaching field. If you're seeing this, it's almost definitely time to get your septic system pumped.
YOU START SMELLING YOUR SEPTIC SYSTEM

Similar to pooling water, if you start to smell your septic system, it's probably a sign that it's time to get it pumped out. Working properly, your septic system should be discharging liquids into your leaching field significantly below ground level and at a rate which at which it can be easily absorbed into the earth. Working properly, this should prohibit any foul odors. If you ARE smelling it, it generally means that your near capacity and liquid waste is being forced to exit the system quicker than it should.
LEACHING FIELD GRASS APPEARS EXTRA HEALTHY

We all love some nice green grass, but if lawn is only seeing this very green grass over your drainage field, you're going to want to get your septic system looked at. Similar to smelling your system and seeing pooling water, generally very green grass over your leaching field means water levels are too high and indicates a septic failure of some sort. It could also indicate excess nitrates from sewage waste, also an indication that the system is not working properly.