Of course it helps if you don't have a family to support.
The world is not a static place. That thing you really want to see might not exist a few years from now. You can visit the same city a half dozen times and have a half dozen different experiences of the place because the world has changed it between visits. I'd rather take a few long weekends every year than save up for one big trip sometime a decade from now, but that's just me.
I'm not sure about where you are, but even someone in the US, working full time at McDonalds, making $6 an hour, could afford a week long trip every year by putting away 10% of each paycheck. $1200 is (roughly) enough for a week long trip to most of the non-tourist packed places, and you can save that up by putting away a little more than $20 a week. Just making lunch at home rather than eating out (or buying a pre-made lunch) can save you almost that much. Its just a matter (like he said) of priorities. That isn't to say that some people can't afford it. My example assumed someone with no family, medical problems, or other large expenses, but it was also a fairly low end of the pay scale (for the US).
CouchSurfing and equivalents can drastically cut your accommodation expenses. Hitch-hiking or cycling give you free travel. Even travelling by bus can be remarkably cheap in most countries if you go the slow way (which also lets you see much more of the country that just the capital) - you can often go 50-100km for a couple of euros. Your primary cost is food, and if you've learned to cook even a few basic meals, you can easily get by on a couple of euros a day.
In Africa, Southeast Asia, or Central America, you can live on $5-$20/day depending on where you go. Hitching through Malawi will run you $3/day tops. Assuming you've ditched your rent/car payments/etc. back home, you're going to be living an order of magnitude cheaper than you would if you simply stayed in the USA.
For short trips, your flight will be the dominant cost. For long trips, you're just not going to spend that much.
If you can put away a measly ten grand, you can stay gone for a long time. How much did you make this year? More to the point, why didn't you manage to save at least $10k of it?