I assume its OK to keep fertilizing annuals in September to help keep them blooming as long as possible, but what about perennials – are there any perennials that should be fertilized at this time of the year (to help overwintering, next year’s blooms, etc)? 

The timing of fertilizer applications on herbaceous perennials is indeed important. Problems arise when nitrogen fertilizers, applied late in the growing season, stimulate new growth when plants naturally want to go dormant. With all but a few exceptions, most perennials do quite well with a light annual application of a balanced granular fertilizer in the spring. Perennials that are either heavy feeders, such as delphiniums, or those that are in bloom for a long period of time, may require additional fertilizer in the middle of their growing season. A little experience will help you recognize when a particular plant has that “hungry” look. This simple fertilizer regime will assure you that your plants are going into winter dormancy in good condition.