Some of my best backpacking experiences have been in storms. I love being on the trail and seeing a huge storm blow in from below and just experiencing the power of nature.
Being waterproof is the key. There's no need to splurge on gear, just take a handful of large garbage sacks. I also second a poncho that can cover your pack as well. I've got a pretty nice rain jacket from Cabelas, but after a few hours in the rain, water finds its way through. A large plastic or sealed fabric poncho is better. I also like the kind that cover my hands and go at least to my knees. I always wear a ball cap, but I spray it down with Camp Dry or something too, I'm satisfied with this for keeping rain out of my face. Also, don't underestimate how cold a rainstorm can be, have your warm layer at the top of your pack with your rain gear.
It always surprises me how much a large tree can keep the rain off. Leaning or hanging your pack in a big full tree will keep it pretty dry, but it's just as easy to throw a garbage bag over it. Also, it should be obvious to pitch your tent on high ground with a mild slope, and never dig a trench around it.
Barring any lightning, whiteout, or other dangerous weather, I hate spending time sitting in my tent doing nothing. I think a positive attitude and embracing the weather is a great idea. I'll just keep fishing or hiking, or look for wildlife because the mountains are a whole new world during a storm.
I was camping on Boulder Mt. in central UT and a foggy snow storm came up in June. My cousin and I, rather than sit in camp, went hiking off through the woods and because of the snow, we could move around silently. We ran into moose, rabbits, a lot of unique birds, and other small animals who all seemed to be waiting out the storm under shelter of trees. It was really something to behold.
I've been stuck a few times on high altitude ridges or summits when a thunderstorm has picked up, and although I was scared spitless at the lightning crashing down all around, I still had to appreciate the really awesome spectacle.