Let's get one thing straight. Although I'm certainly fortunate when it comes to money, I'm not rich by any stretch of the imagination (at least not by North-American standards). I'm able to travel frequently for two main reasons: one, it's a priority for me and I'll skimp on other luxury items (fancy dinners, a flashy car, expensive haircuts, bejewelled Katy-Perry teeth?) to make it happen; and two, I'm one half of a d.i.n.k. Before I begin, I feel it's important to acknowledge that having two incomes and no children not only frees up a lot of money for travel, but also makes finding the time to do so a hell of a lot easier. However, this is not a guide on how not to have children and party every night in exotic locations (or whatever it is you assume child-free adults do), but one on how to put aside money for travel, whatever your current financial and offspring situation.
First, set aside actual money for those trips. This is simple and obvious, but many people don't, and it cushions the bank account blow when you're checking your statement the month after a trip. Chris and I have various savings accounts - general, retirement, emergency, home and travel. Every month, money is automatically transferred from our chequing into these various accounts. How much you allocate to travel will depend on your income and cost of living, but you'd be surprised to see how quickly the money adds up. Because the money is transferred automatically, it's pretty painless, and suddenly you have the money for a plane ticket, hotel stay, souvenirs, whatever. Then, when the time comes to pay for trip expenses, you transfer the money back into your main account to balance things out. This reduces the post-trip bank-balance nose dive.
Second, use credit cards, Airmiles, Aeroplan and the like strategically to help meet your travel goals. This is one you have to be careful about, since it really only makes sense to gain rewards on things you actually need and already buy, but if you can be honest with yourself and are diligent about watching for sales and promotions, the points can really add up. And again, it requires only a little effort and mindfulness, then bam! (seems like a) free trip! And seeming is the same as reality, right? ;)