The resistor is needed if you want to have any say whatsoever in how bright your LEDs are, not to mention to prevent you from accidentally letting the magic smoke out. Check the data sheets for your LEDs, they'll have a forward voltage drop listed. Figure out how many lights you need, in series you have a total forward voltage drop of N * Vd.
At this point, if you don't care too much about repeatable amounts of illumination, you can just take however much voltage you have left in your 9V, divide by the amount of lighting current you want, and place a resistor of that size in the series to set the current. This will work quasi-well. The problem is that a 9V battery is really a 9V _nominal_ battery, and will usually start around 9.5V or so and make it down below
7 by the end of it's life. If you want more regulation over the intensity than those numbers provide, and/or to run the battery farther down before it dies, you're going to need to be more creative. Linear regulated current sources are fairly simple to do (though substantially more complicated than a string of LEDs, a resistor, and a battery) and will give you better brightess constancy. To really use as much of the battery as there is you'll need to go to a switching regulator, which is even more complicated and which, judging from your initial post, you will most likely not be able to get to work.So to answer your question in short, maybe.