Everyone is affected by weeds, either directly or indirectly. It may be through an increase in the cost of food or electrical power, or by getting stuck by burrs and thistles as you walk home. However weeds impact you, it's only going to get worse. The following are just a few examples of how you may be affected in the future:

Personal
Human Health: Over 50 million people are affected by allergies, a large number of which are caused by weeds. Hospitalization and death has occurred due to weeds (poison hemlock, bitter nightshade, poison ivy/oak, blue spurge). Recreation: A number of recreation activities are impacted by weeds. A few of these are: boating, swimming (e.g. hydrilla), fishing (e.g. scotch thistle), hunting, equestrian, hiking (e.g. yellow starthistle), mountain biking, and rock climbing (e.g. puncture vine, thistle).

Money Weeds make you pay, either directly or indirectly.

Transportation: Millions of dollars are spent each year to control weeds around highways, railroads, and airports. Weeds cause asphalt breakup, visibility problems, and increase fire risk.
Industrial/Utility Sites: Weeds impede access, increase fire danger, and in some cases cause physical damage to structures and telephone/power lines (e.g. kudzu).
Drainage/Sewer Lines: Root systems clog and break pipes.
Property Values: Property that has noxious weeds on it can drop in value (due to future management costs). Some ranch and farm lands have become close to worthless in value.

Environmental Impacts on the environment affect us indirectly.
Fire Hazard: Weeds cause range and wildland wildfires to increase in speed, intensity, and frequency. Rural and suburbian homes will be affected. Weed-choked vacant lots also increase fire risk (cheetgrass, medusahead, kochia). Watershed: Increased runoff causes flooding. Increased erosion and siltation impacts aquatic life and affects your drinking water (spotted knapweed, leafy spurge).
Species Diversity: Weeds often force out native plants. Wildlife are forced to leave or die with the loss of their food source and shelter.

What can you do about it?

Noxious Weed Lists (by state)
Other sites introducing Noxious weeds
The status of weeds in the US