The obvious and pedantic answer is that every single character on Star Trek has traveled into the future without a future intermediary: the arrow of time normally only goes one way (into the future). Everything—in Star Trek and out (with caveats)—travels forward in time at a rate of one second per second.
The less obvious (although possibly just as pedantic) answer is that you overlooked special relativity1.
Special relativity
Special relativity establishes that there is no absolute reference frame by which to judge events. What that means is that each frame of reference is judged relative to all others, and that there is no one universal timeline by which to judge whether an event counts as forward (or backward) time travel.
Or more formally, there are two postulates of special relativity:
The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.
Time dilation
One of the consequences of this is that if one frame of reference is moving in relation to another frame of reference, a phenomenon called time dilation occurs. The larger the difference in velocity, the larger this dilation is.
What is time dilation? There's a classic example of a person standing on Earth, watching a rocket fly by. On that rocket, there's another person. Both the person on Earth and the person in the rocket have watches on that are working correctly: one second on the watch is exactly one SI second.
However, if the person on Earth had such crazy vision he could see the watch on the rocket man, he'd notice the rocket man's watch is slower than his, if only by a little bit. Conversely, the rocket man would notice the Earth man's watch has sped up, if only by a little bit.
This is because of both postulates of special relativity at play: the laws of physics are not affected for any one frame of reference (time moves forward in each frame of reference as fast as it always does) and that the speed of light does not change between frames of reference. Because the rocket man is moving faster relative to the Earth man, his frame of reference appears to be slower to the Earth man, and because the Earth man is moving slower relative to the rocket man, his frame of reference appears to be faster.
It's all very confusing, so I'll let Carl Sagan clarify.
Enterprise, time ship
What does this have to do with Star Trek and time travel? Consider being aboard the Enterprise: you're going several hundred times the speed of light. What might be a week-long trip for you (in that you only felt the effects of time, including aging, for a week) would be several years on a more slowly-moving frame of reference (like Earth). For the cost of a cabin on a starship, you'd be able to travel forward in time much faster than the ruffians back on Earth: aging only slightly while Earth's history passes right by.
Plot holes
Now of course, this doesn't happen on Star Trek: there aren't many (if any) plots where the Enterprise arrives back on Earth only to find it's 500 years into the future. And of course, special relativity—and its establishment of universal speed limit—is seemingly ignored with the warp drive.
One popular way to account for this is the Alcubierre drive, wherein the ship stays stationary, but the spacetime around the ship bends and propels the ship faster than the speed of light. Since the ship remains stationary, special relativity isn't violated and time dilation doesn't occur. A ship traveling at warp for one week would experience the same effects as a person remaining on Earth for one week.
Impulse drives
But we're not out of the woods yet: while the warp drive might not be affected by time dilation, there's still the matter of the impulse drive. Impulse drives are "conventional" (as much as that word can be used when talking about Star Trek) drives that propel objects at subluminal speeds.
Since they don't violate special relativity and most definitely increase the velocity of the objects they propel (magnitudes of up to very large fractions of the speed of light), time dilation occurs. So every time the Enterprise falls back to impulse, her crew is traveling into the future faster (relative to other, more stationary frames of reference), if only by a little bit.
Note 1 I am not a physicist, I am a layman. While I believe what follows is mostly accurate, I am most certainly glossing over many of the details and oversimplifying things. Those details should not affect the overall conclusion presented, though.