Good advice here, and I’ll plug swimming as good exercise. It works lots of muscle groups from head-to-toe, especially if you change up your strokes, and is very low impact on muscles and joints. It keeps the icky/sweaty factor down, but if you do much of it, you may wind up smelling of chlorine, or getting Swimmer’s Ear.
You can do it fast for cardio, or slow for fat burn.
It doesn’t do much for flexibility though, so a good regimen of stretching exercises to go along with it will help.
I am 67 and walk my dogs 2 to 5 miles every day in the park. Lately it has been through snow. I also play 8 to 10 hours of racquetball every week. I play with a group of oldsters and we have been playing together for over 20 years. Summer, winter ,it does not matter. get moving and don’t stop. If you do you rust.
Eat a lot of high fat food and be a couch potato = Spry Vegetable Shortening - Wikipedia
Part mental, part physical:
Learn to toughen up. The slow process of learning to accept pain and uncomfortable positions, removing it from your mind, and moving on is vital. If you are a baby about things now, then start taking measures to slowly build up your tolerance. Most spry elderly people I know had moderately physical jobs that they worked at for many years. They continue to stay active, and refuse to accept minor discomfort as a reason to stop. They do their own gardening, sweeping or snow shoveling. They carry their own groceries, and reasonably weighted bags/ purchases. They park farther and walk, even when it is cold/ hot out. They don’t allow themselves to become old in their mind. They don’t give in to the slippery slope of minor creature comforts that eventually leads to jackets in 75 degree weather and dinner at 4.
There is a lot to be said for that philosophy, provided you don’t take it so far that you don’t seek medical help when there is a serious problem to be addressed.
One aged scholar had this to say on the subject:
Basically, if you’re lazy, your physical health is going to suffer from it… and usually it happens before you’re old. I know people in their 20s who already have issues caused by not moving their bodies more than they absolutely have to (I’m not talking about gaining weight, either - it’s mostly joint and back issues and pain, and injuries incurred when they finally have to move more than they are accustomed to).
I will be the next person to endorse the idea of doing some low impact exercise like walking or swimming. Being involved in such activities does seem to be a common theme with the healthier and more mentally alert 80 and 90-something people I’ve treated in my career.
May I recommend a book that you’re currently too young for, but that gives (imho) good advice?
Its advice boils down to:
Damn. I’ve been having good craps and quitting my relationships.
As others have said, a big factor is not abusing your body in your 20s, 30s, 40s, etc. The fact that standing and walking on concrete all day in bad shoes, or high impact sports, or whatever doesn’t hurt now doesn’t mean it isn’t slowly destroying your body and will catch up to you when you are geriatric.
Enjoy everything you want, in moderation, and do whatever you want, in moderation. Because you may spend your whole life exercising and doing everything just right, and then get bone cancer when you’re 66, and die by 69, like my mother. 
Another vote for strength training, which I understand increases bone density in addition to the many other health benefits.
Yoga and Tai Chi and Pilates have been mentioned already. This can be expanded to include most martial arts as really good for cardio, strength, and flexibility.
There are some like Brazilian Ju Jitsu and Mixed Martial Arts that probably should be avoided as they tend to be brutal on the joints.
Eat healthy overall. Don’t be afraid to eat something unhealthy occasionally.
Stay in shape. Doesn’t mean you have to work out every day, but stay active. Avoid high-impact activities that stress your joints too much because you’ll pay for it later. Don’t do too much heavy lifting. Don’t feel ashamed to get help lifting heavy items, your back will thank you later.
Most of the advantages of fencing as a sport that you describe in your post also apply to ballroom dancing, and I have also noticed that serious dancers can continue to dance very well to a relatively advanced age. (Note that I’m talking about serious dancing, not shuffling around the floor at somebody’s wedding - although that’s not such a terrible place to get started.) It also has the advantage of being a life skill that most of us get more chances to practice socially than fencing. 
I can’t overemplasise the benefits of yoga as you age. it’ll not only keep you flexible, but can help your posture. How many old people have you seen that can’t even look you in the eye? Their heads are stuck in a downcast position. Sometime it is due to an actual condition, but it’s frequently a bad, hunched posture carried over years.
Also, don’t crash diet. You frequently loose the connective tissue cushioning fats before fat in the undesirable areas - causing joint stress.
And most importantly, Food.
Most people don’t give it enough importance, but we litterally are what we eat. Food consumption nourishes and directly influences our immune systems, metabolism, growth rate, decay rate, etc.
Be extra vigilent about what you eat and what chemical products you use. i know i’ll get lots of flak here about this… but when it comes to safety, you should actually listen to the concerns of the most-paranoid (those “anti-science” Europeans, Naturopaths, other corporate watchdog groups). the FDA is corrupt and beholden to private corporations. The actually independent groups, using actual user experience and anecdotal data from health practitioners, typically know when something is dangerous or toxic, even if it’ll take years for the FDA to accept the toxicity of said chemical/food. For example, my naturopath told me to stop using plasic tupperware almost 20 years ago and use stainless-steel water bottles - before it was in the mainstream news that a LOT of plasic is toxic. Google Phthalates, bisphenol, or BPA. BPA was declared toxic in Canada. But the, um, american BPA isn’t toxic. Yeah, right. I’m happy that I “overreacted” and reduced my exposure.
See:
http://www.ehow.com/list_7482248_plastic-bottles-toxic.html
http://toxictort.lawyercentral.com/Plastic-Chemical-BPA-Declared-Toxic-In-C-Legal-News--14-195252.html
Also, google ‘Aspartame toxicity’ or ‘Aspartame side effects’. It’s the most complained about item to the FDA, has been demonstrated to become a neurotoxin when metabolized, yet still isn’t banned.
http://aspartame.mercola.com/
Another terrifying fact… read the label - aspertame should never be heated or used in cooking. Geez I hope those unrefrigerated trucks carrying your diet coke across the county don’t count. Except they do.
And shit, Teflon will kill your birds. (think of the whole ‘canary in the mineshaft’ warning system). The EPA has finally asked DuPont to start phasing it out. Shit!! what about the decades and decades people were using this? I’m happy I stopped using non-stick and switched to Cast Iron or stainless steel a while back… you should do the same! Even if “science” doesn’t fully understand the side effects, or the mechanism, I’d avoid 'em anyways!
http://www.ewg.org/node/21780
Other food additives, specifically coloring agents, have been proved to greatly effect neurochemistry!
So what should you do? Listen to the overly cautious. Should you be eating GM corn, or the recently approved cloned meat? I know I wouldn’t. How could they possibly have been doing studies to find out the long-term effects of these foods? They simply haven’t had enough time. Our testing process for food and drugs is compromised by the private corporations that have financial interests in furthering their own goals, not ours.
Organ Damage In Rats From Monsanto GMO Corn
http://www.freerepublic.com/focus/news/2427373/posts
Check out this site:
Yes, they’re “natural” proponents - which might turn some people off, but really, those types of practitioners are usually more up on this then your average g.p.
Oh yeah, unless you’re immune compromised, don’t get the flu shot. Or at least demand one without any of the neurotoxin Mercury (called Thermasol - it’s used as a preservative, so they can use multiple dose bottles, saving themselves money).
Good luck.
Watch what exercises you do. I did some military presses in my mid 20’s and blew out my shoulder joints. They’ll never be the same again.
Stick to the basics or whatever a trainer recommends.
I think what you mean is Thiomersal. Yeah sounds like it’s bad stuff used for a good purpose.
I too err on the side of caution. I think too many things are done by companies for cost, appearance, and convenience that aren’t particularly good choices for health.
Yep. Get moderate exercise on a regular basis. Walk briskly (it takes no special clothing or euiptment) 20 minutes twice a day. A nice little walk also get you away from your desk, which is good for several reasons. It’s all too common to join a gym, work out like crazy for a month, then stop.:rolleyes: Instead, just walk- briskly. Get your fat ass out of the car. If whatever errand you can do is a 30 minute walk, then walk, instead of drive. Ok, buy a dumb-bell or two, keep one at your desk one at home to get in a little upper body stuff, if you like.
Don’t eat junk or fast food. Meat is good for you- in moderation, but you likely don’t eat enough veggies, whole grains or get enough fiber. No chips, no candy- altho a little dark chooclate is good for you.
Maybe try some Reservetol from red wines. Drink in moderation only.
Get enough sleep.
Don’t smoke.
I am not a real Doctor.
Important point. I disagree that there are certain exercises we should all avoid - I do military presses all the time now, but I also tend to have weak shoulders which are prone to mild tendonitis, and it’s been a very slow and careful process working up to doing any sort of presses with real weight. When exercising it’s very, very important to take things very slowly, use proper form (and don’t do anything you can’t do right), and NOT to push your body to the limit. If it hurts - stop. That goes for strength training and for cardio - I know an awful lot of people who’ve seriously injured the joints and/or tendons in their legs from overuse while running, or using various exercise machines.
Do whatever you can to avoid getting injured, because sports/exercise injuries can be serious and have a really terrible effect on your whole life.