First the official rule in 3.5.
Jumping during a Charge
You can make a long jump to avoid an obstacle as part of a charge, as long as you continue to meet all other criteria for making a charge before, during, and after the jump.
(Rules Compendium p.27)
Though there is some debate on the issue of whether the Rules Compendium takes precedence over a core book. WotC intent was clear when they wrote:
The book you hold in your hands is the definitive guide for how to play the 3.5 revision of the DUNGEONS & DRAGONS Roleplaying Game. Years in the making, it gathers resources from a wide variety of supplements, rules errata, and rules clarifications to provide an authoritative guide for playing the D&D game. It updates and elucidates the rules, as well as expanding on them in ways that make it more fun and easier to play. When a preexisting core book or supplement differs with the rules herein, Rules Compendium is meant to take precedence. If you have a question on how to play D&D at the table, this book is meant to answer that question. (Rules Compendium p.5)
This doesn't mean that the Rules Compendium (like most of WotC rulebooks) always phrases the rules in the best manner possible. Notice how only an obstacle is mentioned in the first quote above. There is nothing about jumping over difficult terrain. But in the initiating a charge section obstacles aren't even mentioned.
If any line from your starting space to the ending space passes through a square that blocks movement, is difficult terrain, or contains a creature (not a helpless one), you can’t charge. (Rules Compendium p.27)
This is where the 3.5 FAQ is helpful in clarifying this particular rule. Though one must take care when using the FAQ. (see here):
Can my character make a jumping charge attack, either with a long jump or a high jump?
You can make a long jump as part of a charge. You must still follow all the normal rules for making a charge, such as moving in a straight line on the battle grid. This tactic can let you avoid some of the normal restrictions against charging. If a square of difficult terrain is between you and your charge target, you could possibly jump over it with a long jump. (The fact that your jump means that your movement isn’t a perfectly
straight line doesn’t make the charge illegal—you’re still moving in a straight line as far as the battle grid is concerned, and the jump isn’t really changing your direction.) (D&D FAQ v.3.5 Update Version: 6/30/08 p.72)
Now for Pathfinder.
I haven't seen it explicitly mentioned in any of the books. So here's the best information on the topic that I'm aware of.
On the Paizo forums this question was asked (the original includes the 3.5 FAQ quote above)
Can you jump over difficult terrain with your mount, while charging?
The 3.5 FAQ says that you can, but official word would be nice!
In agreement with the 3.5 FAQ, James Jacobs (Paizo Creative Director) states
Nothing's changed here, really. Jumping is a part of movement. If you're charging and part of that charge needs to be a jump, that's fine. You'll just need to make the appropriate Acrobatics DC to make the jump; if you fail the jump, obviously your charge is wasted.
On his post it states
10 people marked this as FAQ candidate. Staff response: no reply required.
Apparently Paizo didn't take issue with James statement.