Make sure your quick release levers are closed and tight.
Few things are more terrifying while riding than having your front wheel, fork or handlebars fail—there is simply nothing you can do to prevent the inevitable header. The simplest way to avoid this is to make sure that your quick release levers are closed and tight. Do not just look, grab the lever and ensure it is firmly in the closed position.
Check the tire pressure—or simply inflate them fully.
Tires in good condition lose pressure slowly, so you want to make sure they are fully inflated for each ride, but you also want to check that there are not any slow leaks that have made them go flat in the last day or so.
Check your tires for damage.
Normal wear on your tires can lead to cuts, slices, and bare casing (the woven material normally covered by rubber). While little nicks are not often a concern for your training tires, it's good to keep an eye on them. Cuts or slices can allow your inner tube to bulge out, which is sure to lead to a flat in very little time. You need to replace your tire ASAP. Similarly, if you see casing coming through your rubber, it's time for new tires.
Make sure your brakes' release lever is closed.
If you have transported your bike recently, you may have attached your wheels but not flipped the brake's release lever back down (circled in image).
Double-check this so you don't grab for your brakes and find (next to) nothing.Check that your wheels are centered in the frame, are true, and brake pads do not rub.
Look at your wheels and make sure they are centered in the frame (see image of front wheel off-center in fork). If a wheel is not centered, loosen the quick release lever, center the wheel appropriately, and tighten the lever again. Then spin each wheel looking to see that the wheel is true (doesn't wobble from side to side) and that your brake pads do not rub at all. If necessary, adjust your brakes so the pads are properly centered. If you are not able to center them to avoid the rim rubbing at some point in its revolution, then your rim needs to be trued. If you know how to do this, great! Otherwise, find out how or take it to a local bike shop.