A weak market is a challenging environment in which to sell a home. With the availability of homes for sale - and the lack of buyers - sellers need to be realistic.
Be realistic on your initial pricing - if homes are moving slowly you are very unlikely to secure a premium price unless your home is extraordinary (or you get very lucky).
Consider lowering the price if you are not getting showings or offers. Don't take offense at insulting offers - simply counter-offer or politely decline. Remember that buyers are being constantly told the market is weak and they should "get a deal."
Consider a buyer's quality level when assessing sub-standard offers. If a buyer is pre-qualified and ready to close it may be worth accepting a little less.
If you have the flexibility, consider waiting. These markets are usually followed by recovery periods, when more buyers enter the market and prices stabilize and begin to rise.