1. The straps are digging into your shoulders, leaving grooves and marks.
Most of the support that the bra gives should be from the band of the bra - very little weight should be on the shoulders. Straps digging in to your shoulders indicate that too much weight is being placed there. This can cause discomfort, pain, slouching, and marks/shoulder grooves (that can even become permanent)!
If you have straps digging in and leaving marks, this probably indicates that the band of the bra isn't tight enough to give support. Go down a band size (and up a cup size for each band size) until the band is firm and supportive and you can just fit two fingers under it.
2. The wires are sitting on breast tissue.
The wires should fully encase the breast tissue on all sides of the bra. Wires sitting on breast tissue will lead to shifting, much readjusting, an ill-fitting look, pain, unwanted re-distribution of breast tissue, and all sorts of other problems!
If wires are sitting on your breasts, go up as many cup sizes as needed in order get the wires sitting comfortably against your ribcage and have the breast tissue fully encased.
3. The center gore of the bra isn't firm against your sternum (or isn't touching at all)
Relating to #2 - a center gore that doesn't sit comfortably against your sternum (you shouldn't be able to fit fingers under it) indicates too-small cups and probably a too-large band.
yet another example *tsks at Playtex*)
Go up in cup size (and down in back size if necessary) until the center gore sits completely against the sternum and no wires are resting on any breast tissue.
4. The band is riding up in the back (or is sitting too low)
This is one of the most common problems women have - a too-big band and too-small cups. The band riding up in the back (or sitting too low on the back) indicates that the breasts are not supported by the bra - the bra is functioning more like a sling rather than giving firm support for the breasts. The band of a new bra should be sitting straight and firm across the back on the loosest hook.
Other indicators of a too-big band are if you can fit more than a couple of fingers under it, or if you're always having to hook the bra on the tightest hook.
Go down in back size (and up a cup size each time) until the band sits firmly across your back. You may find need to go up additional cup sizes as well at the end, as it's difficult to see how well the cups are fitting if the band is much too large. For example, when I got properly fitted for the first time, I went from a 36DD to a 30G (a 36DD cup volume is roughly equal to 34E, 32F, and 30FF, so I went up an additional cup size once the band size was correct).
5. Your boobs are bulging out of the cups, creating the "quad-boob" (or four-boob) effect.
This may also mean that the wires are sitting on breast tissue (see #2). Boobs bulging out of the top of the cup indicate that the cup is too small. There's nothing wrong with some cleavage, but it should be a smooth line that the bra creates, not bulging.
Go up in cup size until you no longer get bulging out of the bra.
Got questions about proper fit? I'd love to hear them!
(Note: You'll notice that many of these examples are either Playtex or Victoria's Secret models/bras. It irks me to no end that neither of these two companies can even fit their models correctly!)