Traveling with photo gear is much harder than it used to be. Airport security is becoming more and more restrictive. US airport security now has a ban on carrying rechargeable batteries without a container: they must be in a case and not loose in your bag. Multiply this with airport security staff of little understanding and the full authority of Homeland Security, and life can be difficult. So what can you do to minimize traveling friction and get yourself and your gear to your destination safely?
Aim to carry on your photographic gear as it is best protected and handled by yourself rather than in checked baggage. Unfortunately, there are more and more restrictions on the number and weight of carry-on items, especially on international flights. If you are going to carry a heavy camera and lenses in hand baggage, it is essential to find the restrictions on hand baggage weight beforehand. Go to the airline's website and read the small print. British Airways has no restrictions on hand baggage weight, while Virgin Atlantic has a 6kg (roughly 12lbs) limit. I have found that Air France is particularly strict and inflexible when it comes to carry on baggage weight, so I try to avoid traveling with them if possible for this reason.
You also need to check carry on items limits, which can be different when returning vs. flying out, and the UK is particularly problematic as different airlines have different policies. Some airlines even have different rules depending on your departure airport. For example, when flying Virgin Atlantic to London Gatwick from the US, you can take two carry on items. Flying from London Gatwick you're allowed one. But if flying from London Heathrow, you can take two! Check the airline website or call the airline in advance, tell them where you are flying to and from, and find out.
I pack non-fragile photographic paraphernalia in Zip-lock bags in the middle of a suitcase so that it's protected from moisture and shock. I carry by carbon fiber (lightweight) mono-pod this way too, along with brushes, filters, batteries, chargers, cables and the other non-valuable odds and ends. That leaves my carry-on for the most fragile and expensive gear: cameras and lenses.
Professional photographers typically carry insurance for their gear and liability. For non-professionals, check your household insurance policy. It typically covers possessions taken outside the home, with exclusions or limits for expensive items such as cameras -- check to see what's covered before buying extra insurance.
Finally, I also keep a minimal set of chargers and cables in my carry-on bag in case checked bags are lost -- anything that I can't re-buy easily at the destination. Airlines are now losing more bags per thousand carried than ever before, and when it happens, there's no guarantee you'll get your bags during your trip. After losing my bag on a direct flight recently, United Airlines returned it four weeks later, tattered and torn.
The golden rule of travel photography remains "keep your camera with you at all times", and that includes your flights too.