Tents of all types and ages require some weatherproofing. Even expensive four-season shelters develop cracks in their armor, which is why every tent owner should set aside an hour or so each spring for some simple preventive maintenance. Not every seam on the tent needs to be waterproof, only those that will be exposed to rain, runoff, or puddles. This always includes seams on the fly and tent floor, but usually not on the tent canopy. Because seams on the interior walls border porous panels of mesh and uncoated nylon, treatment of these seams offers little additional protection, so don't waste your time.
Many new tents come with factory-taped floor and fly seams, which is a big plus.
A simple visual check will reveal if your seams are taped. They'll have a smooth feel and glossy appearance, as if someone ironed a thin strip of translucent packing tape over the threads. Taped seams don't require additional waterproofing. Untaped exposed seams, on the other hand, have thousands of tiny needle holes that are prone to leaking. You'll need a tube of seam sealer, a polyurethane glue that seeps into every crevice and forms a watertight barrier as it dries.