Creatures may have modes of movement other than walking and running. These are natural, not magical, unless specifically noted in a monster description.
Burrow: A creature with a burrow speed can tunnel through dirt, but not through rock unless the descriptive text says otherwise. Creatures cannot charge or run while burrowing. Most burrowing creatures do not leave behind tunnels other creatures can use (either because the material they tunnel through fills in behind them or because they do not actually dislocate any material when burrowing); see the individual creature descriptions for details.
Climb: A creature with a climb speed has a +8 racial bonus on all Climb checks. The creature must make a Climb check to climb any wall or slope with a DC of more than 0, but it always can choose to take 10 (see Checks without Rolls, page 65 of the Player's Handbook), even if rushed or threatened while climbing. The creature climbs at the given speed while climbing. If it chooses an accelerated climb (see the Climb skill, page 69 of the Player's Handbook), it moves at double the given climb speed (or its base land speed, whichever is lower) and makes a single Climb check at a -5 penalty. Creatures cannot run while climbing. A creature retains its Dexterity bonus to Armor Class (if any) while climbing, and opponents get no special bonus on their attacks against a climbing creature.
Fly: A creature with a fly speed can move through the air at the indicated speed if carrying no more than a light load; see Carrying Capacity, page 161 of the Player's Handbook. (Note that medium armor does not necessarily constitute a medium load.) All fly speeds include a parenthetical note indicating maneuverability, as follows:
Perfect: The creature can perform almost any aerial maneuver it wishes. It moves through the air as well as a human moves over smooth ground.
Good: The creature is very agile in the air (like a housefly or a hummingbird), but cannot change direction as readily as those with perfect maneuverability.
Average: The creature can fly as adroitly as a small bird.
Poor: The creature flies as well as a very large bird.
Clumsy: The creature can barely maneuver at all.
A creature that flies can make dive attacks. A dive attack works just like a charge, but the diving creature must move a minimum of 30 feet and descend at least 10 feet. It can make only claw or talon attacks, but these deal double damage. A creature can use the run action while flying, provided it flies in a straight line.
For more information, see Tactical Aerial Movement, page 20 of the Dungeon Master's Guide.
Swim: A creature with a swim speed can move through water at its swim speed without making Swim checks. It has a +8 racial bonus on any Swim check to perform some special action or avoid a hazard. The creature always can choose to take 10 on a Swim check, even if distracted or endangered. The creature can use the run action while swimming, provided it swims in a straight line.