There are actually two trains of thought on this:
1. Bid your max. If you really want the item, bid very high, and you will probably get it. The only issue here is that the seller could send someone to bid the item up to inflate the price - it can be risky. Also, using this method invites additional bids from potential buyers who get caught up in the bidding process - they will often bid higher than normal because of the activity. The bidding activity will also attract additional bidders.
2. Bid within the last 10 seconds of the auction. You'll need to use a robo-bidder or wait it out. Open a second browser window with your max bid, username and password pre-loaded, so all you have to do is click the process button. Use the first window to refresh the page periodically and use a timer or countdown. When you get to 10 or so seconds, mash the process button in the second window. This will prevent other last minute bidders from having the chance of throwing in another bid. These many times become the most satisfying if you have the time to use this method. I've beaten many known shill bidders (this is when the seller uses friends or alternate IDs to bid up the price) because the high bidder or seller is thinkng that the bidding has stopped. The danger here is when another bidder is using exactly the same method, and they input a higher bid than you.
In the final analysis, if you use a combination of both methods you'll have the highest success. You have to adapt your technique to the type of item and the amount of demand. You should also study what is happening with the bidding on similar items to see what you are up against. I know it all sounds crazy and involved, but I've saved literally hundreds of dollars on some items by using smart techniques like these. Check my ID and feedback: http://feedback.ebay.com/ws1/eBayISA...d=johnnyapollo
-- Best, John