bad alternator (brushes, internal regulator, rectifier set, short/open windings), loose belt, bad battery cables, bad alternator wiring/connections, loose/missing grounds.
A little systematic trouble shooting is required, but cleaning and tightening battery terminals (also clean battery top if it needs it) and the grounds at fender wall, alternator, and the one on engine by diagnostic plug are are good ideas anyway. See if you have charging voltage at the battery terminals of 14-15V. Verify state of charge of battery to see if it is going down--should be 12V-12.5+V with engine off. Also check alternator fusible link in engine junction box. That's how I'd start.
Don't ignore it. Battery will keep car running and starting for a short time (at night, less than 30 minutes) until it decides to crump at worst possible time: miles from home, at night, with wipers on due to rain or snow.