Just like the title says, should I be changing my gear every time I level up? Is it worth it? I just started Nightmare mode with my Wizard last night and have kept the same gear on since about the beginning of Act IV of normal mode. I seem to be doing alright on Act I - Nightmare, haven't died yet knock on wood. But I'm afraid I'm going to have to start changing gear again soon. I have plenty of gold to where I could hit up the blacksmith or the AH.
This depends heavily on whether you are playing hardcore or softcore. In softcore, there is no pressure. If you find yourself in trouble and dieing, then you can still lean back and get better gear from the AH (you don't even have to repair the old one ;)
In hardcore, things are very different. You don't get the chance to die once as a reminder to upgrade your gear, so you have to do it more often based on how much life you have left in dangerous encounters and how much damage you did.
Generally, it would be best to have the best gear for your current level. But most players simply can't afford paying outrageous prices in the AH for top-of-the-line gear at every level-up. Therefore, you have to strike a compromise and continuously improve your gear. It might very well happen that you still run with an item that is 10+ levels below your current level, but that item is bound to be replaced as soon as you find something decent in the AH.
You certainly don't need to keep upgrading on every level up. Periodically review your equipment and look to replace the worst piece you have, simplest to look on AH with a small buyout - it won't break your wallet and can give a nice boost.
The only item you want to upgrade more often is your weapon, as your damage will suffer a lot if you are using something from 10 levels earlier. Again, just search for something with your main stat & other preferred traits (for e.g. Life on Hit, Vit) with a reasonable buyout (I'd say 2-5k will get you a decent weapon really cheap)
Also, on using gold for the blacksmith: Note that esp. with weapons, the chances of getting a good roll is quite low. You could try to have some armor crafted, if you're really lucky that can make you rich (or usually, won't be worth what it cost). You can look in the Blizzard crafting forums to find someone who is cheap & has live streaming.