I never outright place my maximum bid because then someone else will try to bid it up, and I end up spending more when I don't have to. I'm not sure how to explain it clearly so here is an example:
An auction that starts at $9.99. I'm willing to pay $50. If I put my max bid at $50, another bidder will come and bid it up to $15. When that doesn't work, they bid up to $20. When that still doesn't work, they go up to $30, and so on. At some point they will either outbid me or decide it isn't worth it and give up. But either way, the price is nowhere near the $9,99 starting price. This is technically the way an auction is "supposed" to work but most users don't do this in my experience. The only time this might be the best idea is if you'll be away from the computer for a long time and you REALLY want the item.
The other method is to bid up in small increments, but you have to be prepared to lose the auction unless you keep a close watch. So using the same example, instead of starting with $50, start with $12. If someone outbids you, bid again just a few dollars higher. This way even if your limit is $50, you might get away with spending less since the other bidders won't be placing higher and higher bids in an attempt to outbid you--they will only need ot bid up 2 or 3 dollars, and you can always place a higher bid later. I don't know if that made any sense at all...
The last and evilest method (which I use and recommend :p) is to just figure out when the auction ends and place your bid in the final few minutes, or sometimes even seconds. The only downside to this is that you have to be glued to your computer during the final moments (I'm lucky since I have an ebay app on my iphone so I can bid from anywhere, and it helps that I have no life right now :p). You can have ebay send you reminders when an auction you're watching is about to end so you don't forget. I almost never lose the auctions I'm bidding on, and when I do, it's usually intentionally (because the price got too high or something like that).
I often use a combination of the last two methods, depending on how popular I anticipate the item will be. If (going back to the example), someone outbids me at $12, instead of placing a new bid right away, I just wait until the last minute to place it.