Two particular fly rod weights seem to rule the industry: the 5 and 8 weight. The reason for this is pretty obvious—they are extremely versatile for a range of species and conditions. From trout to light saltwater, owning these two rods means that you'll be able to cover a lot of bases with a minimal amount of tackle. On the flip side, for most of my fly-fishing life I've been somewhat of an oddball with my rod choices. Why do I say this? I have mostly favored the 7-weight rather than the 8-weight.
To be fair, if you want just one "heavier" rod an 8-weight might serve you better for most situations. Of course, this will vary depending on where and how you fish and what you target. For example, if you just want one rod for, say, freshwater bass, a bit of striper fishing, and a yearly bonefishing trip, I'd pick the 8 weight. It'll handle bulkier flies and wind a bit better, and it should be a little stouter for bigger fish. With that said, in my humble opinion the 7-weight shouldn't be ignored for a few solid reasons:
Casting: For me, a 7-weight is more fun to cast due to the lighter feel. With some exceptions, I like to use the lightest rod possible in a given situation. If the wind isn't blowing hard, a 7-weight works very well and is a little more pleasant for me to fish.
Smaller Fish: I often fish the beaches on the west coast of Florida for snook, and many of these fish in my vicinity are on the small side. The 7-weight makes fighting these little guys more fun and is better for lighter tippets, but still gives me some good pulling power in case I tie into a lunker snook or powerful jack crevalle.
Softer Presentations: Granted, the difference here may not be huge, but dropping down to a WF7F line as opposed to a WF8F gives me a slightly softer presentation which I think helps a lot, especially in shallow water sight-fishing situations when the wind is down.
My very first fly rod was a cheap 7-weight and I've almost always had one in my arsenal since then. An 8-weight may be the more sensible choice to start with for pure versatility, but the 7-weight certainly has its place. Like the title says, "Don't Ignore the 7-weight!"