1. HD was one of if not the original manufacturer of motorcycles. In the early days they made their reputation based on success with motorcycle racing primarily. Similar to the early days of auto racing, people bought vehicles from manufacturers whose products were successful in racing. The company started in 1903. During WWII all production was dedicated to the war effort, which is when the big bikes first started to become popular. Guys came home from the war and wanted a motorcycle like the one they rode in the war. Additionally Hollywood DID NOT do HD any favors. Hollywood portrait bikers in a negative light (The Wild One) and the Hells Angels didn't do anything for their image either. Then in the late 60s'/70's the Japanese bikes hit the US market, which HD lobbied congress to put a tariff on. Eventually declining sales and a poor product reputation caused the company to sell out to AMF. The AMF days were a disaster and the company was bought back by a group of employees lead by Willie G. Davidson - grandson of the founder. That is roughly the time they introduced the evolution engine, which was much more reliable than older engines like the shovel head, pan head, knuckle head and flat head. At this point HD was the only "American" made motorcycle. To answer your question, their strategy was to sell to anyone who wanted a motorcycle, and for years and years they had no competition. There were no image issues until the 1970s - which compounded with quality issues almost put the company out of business.
2. New strategy. Market the "brand", by every means possible. Encourage customization of their motorcycles and those of a similar ilke (i.e. Orange Country Choppers). First and foremost build a high quality motorcycle. One that doesn't require you to pack a lunch for the downtime on the side of the road, which their "70s/80s" bikes had a reputation for. They marketed the bikes to yuppies who were possers for the whole biker image they remember from their youth. Now that the bikes are so reliable, you don't need to know how to fix it, just ride it. Until recently they were getting ~$4K-$5K over list price for the bikes in the new Harley palaces (dealerships) that have popped up all over the country. they purposely produced fewer bikes than the demand for them, which pushed up prices and only further increased demand. They also created the Harley Owners Group (HOG), which promotes safe riding, group riding, charity involvement, community involvement etc.. and local chapters who put on public events to generate charity funds. Hog also puts on huge events for it's membership - see the 105 year anniversary stuff happening in Milwaukee this summer.
3. Media strategy.........they originally funded shows like the Jesse James West Coast chopper show, the biker build offs, Orange Country Chopper show - when it was on Discovery. This created a renewed interest in biking, which HD cashed in. They also pour lots of funding into the motorcycle rallies that happen all over the country - such as Daytona bike week, Myrtle Beach bike week, Americade, Laconia Bike Week, Sturgis etc.. Additionally the HOG club has HD only rallies all over the world every year. For owners, they send out two quarterly magazines - enthusiast (communication about what's new with company, new bikes, stories about trips, customizing etc..) and the HOG magazine (talks about happenings in the HOG organizations globally)
4. Psychological feeling - freedom.
The thing about their bikes is that they appeal to people who aren't comfortable riding all bent over, mostly older people. I disagree about the need to change their bikes to appeal to a younger generation, I see lots and lots of young (early 20s) folks riding traditional Harleys. Their bikes appeal to a lot of people. Not everyone wants to go a zillion miles per hour, some folks want to see what they a riding by. They are very reliable, the dealerships are big, bright, clean and inviting. Sure Honda, Yamaha etc.. make cruiser style bikes - but those are all HD knock-offs (look at them). If your going to buy one of those, you really just want an HD. Similar to the sport bikes, if a sporty is what you want - get one of those, the Japanese make great sport bikes. Sport bikes are a blast to ride, they just don't appeal to a certain segment of the motorcycle buying market. If you want an RV on two wheels, get a Goldwing.
http://en.wikipedia.org/wiki/Harley_Davidson
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You can spend big $ with other manufacturers too. Want to get bent over a barrel - go into a BMW MC shop. Their motor cloths cost upwards of a grand for a jacket. Trust me, HD has nothing on them. Same with the others, it's not so expensive to get into some of the sport bikes, but modify one - bend over. My daughters boyfriend just put $12K into accessories on a brandy new Yamaha R1. Goes real fast, real shinny, loud....sound familiar?