I've always imagined that, unless a creature is taking free actions (hence, also, swift and immediate actions, all of which can be taken in conjunction with other actions), actions are taken sequentially, one action needing to end before another action can begin. However, after trying to puzzle out mounted combat again, I realized maybe I've been limited in my imagination.
While taking a move action to make a normal move to travel up to its speed, can a creature simultaneously, at any point during its movement and without stopping, take a move action that does not involve moving any distance? For example, can a creature take its first move action to make a normal move; take its second move action to, for example, sheathe a weapon or open a door; then continue moving up to the remaining distance from its first move action?
Note: Please show some sympathy for my ignorance if you've always played that Yes is the answer. If you've always played—like I have—that No is the answer, let me explain where I'm coming from. During mounted combat, it's the mount's actual movement that prevents a rider from taking full-round actions that also involve movement, the idea seeming to be that the mount's movement replaces the movement the rider would've taken (so a mount that must travel 10 ft. or more to a foe prevents a full attack by the rider, for instance, because the rider didn't start with a full-round action near enough the foe). However, even if the mount moves, the rider continues to be able to take non-movement move actions at any point along the mount's movement. What I don't know is if this situation is unique to mounted combat or should occur generally.
For example, one of my frustrations as a player and a DM is the difficulty creatures have in getting through doors: opening a door takes a move action, so it takes a creature its entire turn to move 10 ft. up to a closed door and open it. However, if the creature can move 10 ft., open the door, and, say, continue moving 20 ft., that's not nearly the issue it once was.
I've tagged this question rules-as-written as I'd really like to see either position supported by a text as I am uncomfortable extrapolating a general rule from implications alone (for example, the rules for mounted combat, the lack of a move-a-little-then-take-a-move-action-then-move-a-little-more feat similar to the feats Shot on the Run and Spring Attack). Likewise, I've tagged this question pathfinder because, while as a DM I'm more interested in a dnd-3.5 answer, I'm a player in a Pathfinder campaign and that game, a D&D 3.5 offspring, uses an identical turn structure and may have additional information on this topic.