I’m thinking gymnastics as the shortest where, IIRC, you’re pretty much done by your early to mid 20’s or so. Are there any other sports with an even more constrained time window for competitive performance?
Re longest I’m thinking golf, but maybe there are others.
Diving is pretty short term, at the high end of competition.
What about curling? I don’t think age would matter much in that.
Tris
Yachting can be long term.
Bill Northam 1905-1988
Olympic gold medallist 1964 Tokyo Olympics
Skipper 5.5 metre class yacht ‘Barrenjoey’
You can drive a race car from toddlerhood (with low-powered gokarts, of course, not full-sized cars) until your senses fail, although most start in their teens or early 20s and retire by their mid-60s.
Hey astro
I went to second grade in Salisbury Md at the State Teachers College in 1946.
Lived in Newton St - either 221 or 112 - can’t remember exactly that far back- it was a three storey shingle house I think.
Have lived in Melbourne (Australia) since 1947
Chess. Worldclass players range from early teens to well in their seventies.
Longest: various mental sports should qualify; e.g. chess where grandmaster norms are achieved by ages from 13-70+. For something obstensibly more “physical”, I’d go with Gateball (a japanese croquet descendant) which was designed for young children but is most popular among retired folks (and ironically is less physically demanding then mental sports imo).
Shortest: Gymnastics is a pretty good call, tho I’d love for a Little Person to come along and dominate the sport for a good 25 years.
For longest, I can think of a simple one that beats all: running.
Is Russian Roulette a sport? 'cause I’d go with that for shortest.
Really depends on what you consider a sport. But if we’re gonna call chess a sport ( I consider it intellectual competition ) this would be my top 5
chess, age 5 or 6 to senility
billiards, early teens (for skilled play) to seasoned citizen age
golf, teens to 50 or 60 (the walking dropped it to 3rd, need more physical stamina)
Motor sports, late teens to mid-50s (skipping the 30 mph go-carting days of the youth)
curling, teens till paralysis (the thrower just needs aim and enough strength to stay on skates) If I include chess as a sport, why not this one?
I would imagine that most of the competitive events in a rodeo would have a pretty short span. You don’t get young teens competing very often, because of the physical demands of the activity (the need for upper body strength, for example). And I haven’t seen very many older folks competing, since one’s ability to take those kinds of falls tends to diminish rapidly, even in early adulthood. Throw me off an angry bull, and I’m not going to get up, dust myself off, and mosey out of the arena! Definitely stretcher time.
Mostly individual competition has been mentioned. What about team sports? Basketball has a deceptively longish age time-window. You can have players starting in their late-teens and going into their late thirties before retiring. In fact, many players peak at age 30.
I don’t watch the NFL much but I’ve heard that the average NFL career lasts around four seasons. Anyone have any idea?
Equestrian sports.
Take a look at the ages of the people on the 2000 US Olympic equestrian team.
http://sportsillustrated.cnn.com/olympics/news/2000/usteam_equestrian/
It is also one of the only sports where men and women compete on an equal basis.
Shortest time if not Gymnastics is Thai Boxing. The top Thai participants tend to burn out pretty fast. By the time they are 25 they are absolute wrecks.
I’d say Basketball is definetly one of the real physical sports where players can enjoy a top lvl presence.
The Kentucky Derby. Only three-year olds qualify.
Oh, you meant humans? 
FISH
There are a bunch of powerlifters in their 50s and 60s.
That figure may be about right, but I don’t think the NFL qualifies for what the OP means. The AVERAGE NFL career may be short, but it is a function of players not being good enough to play at the pro level, or having to quit due to injuries, rather than age having anything to do with it, per se. If an NFL player has the talent and escapes serious injury, they may hang around into their 40’s - for instance, Jerry Rice, who probably should retire, but is still playing at 41. At wide receiver.
I would say baseball is fairly long as a team sport. One could start in their early 20’s and easily go to their early 40’s. I mean, look at Cal Ripken. As long as you can still hit the ball, and have decent fielding ability, you can stay in the game (assuming you were a well-knwon player beforehand.)
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FWIW, SeekingTruth, in curling you actually don’t wear ice skates - usually just sneakers.
For more info, go here
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I would say that competitive bass fisherman probably have fairly long careers.
For the shorter lived careers, I’m gonna have to go with **rodeo riders **.
KTM
Hockey is another sport where you can play into your 40’s if you’re good enough. Igor Larionov (formerly with the Detroit Red Wings, currently with the New Jersey Devils) is 42, and is still competitive.
I was going to mention hockey. In addition to Larionov- Messier, Chelios, Francis and MacInnis (although injured) are all 40+. And Don’t forget that Gordie Howe finally hung up his skates at the ripe young age of 53.