When deciding what to offer on a home, you need to take into account several things:
1. The value of the house based on comparable recently-sold properties
2. Whether you are dealing with a foreclosure, short-sale or regular sale
3. The history of price drops
4. The condition of the house
5. The value of the house once it is updated

The first item is the most critical. Your Buyer's Agent can help you to determine the current value of the home based on comparable recent sales in the neighborhood. You can compare those properties for condition and features to determine what the house is actually worth on the market. Then you decide what it is worth TO YOU.
If you are dealing with a foreclosure, chances are you can put in a low bid and the bank will counter if they like the other terms of the offer. If it is a short sale and you put in a low bid, you may not know that you are wasting your time for months. If the seller occupies the home, a low bid could insult them and ruin the negotiation process.
Bids should be able to be explained by the Buyer's Agent when presenting the offer to the listing agent. Your Buyer's Agent should be able to say "the buyer is making this offer because..." where the explanation would make sense to the seller. Just putting in a low bid with no justification for it, doesn't make it very desirable.
If the home is in need of updating or major repairs, consider what the home would be worth if it was repaired or updated and base your offer on that price less what it will cost to get it to that condition.
The initial offer on a house can be crucial to an eventual agreement between the seller and the buyer. So work with your Buyer's Agent to make the negotiations acceptable to everyone.