There are many ways to move around the world of RuneScape, as described below.

Foot Power

Walking

The easiest, and by far most common, method of getting around is simply walking to and from different destinations. Please note that walking to a spot can be achieved by clicking on the ground in the main window or by clicking the place on the minimap in the top right-hand corner of the screen. A fairly slow method of transportation, though, walking is usually used for short hops in between close-together cities or inside larger cities.

Running

By going to the user interface and selecting "run", a player can use "energy" to run faster than he normally walks. A player can also hold the Ctrl (Control) and click to run. Energy, which starts out at 100%, is reduced when a player runs. The speed at which it is reduced is determined by the weight that the player is carrying, which is denoted in that interface. Energy slowly regenerates whenever the user is logged on, though this can be sped up by eating strange fruits (+30% energy) or increasing the agility skill for members (increases regeneration speed). The agility skill is one of the few members skills that is used on both non-member and member worlds, making it a handy plus after someone has stopped their membership.

Automatic Teleports

These can be used by members and nonmembers.

By talking to Shantay, south of Al-Kharid, and claiming to be an outlaw, players can also transport to Port Sarim jail.
Some random events can also result in a teleport, such as taking the wrong item from the Sandwich lady, which always results in a random teleport. a few other events can result in a teleport if you get them wrong, but the reward for success is better.
If you carry no more than 3 items (and are not skulled), dying is a quick way to get to Lumbridge (or Falador, for members who have done the Recruitment Drive quest and chosen to return there).
In Al Kharid there is a person with a glider, just south of the toll gate, will transport you to Varrock (for a fee of course) possibly round-trip but at least one-way. (talk to him to find out the price).

Magic Teleports

Using various spells with the Magic skill players can teleport around the world of RuneScape instantly.

Free World

A limited number of teleports are available to non-members:

Varrock teleport (level 25)
Lumbridge teleport (level 31)
Falador teleport (level 37)

Each one requires a law rune, 3 air runes and one other

Members World

All the teleports that work on free worlds also work on member's worlds.

Additional magical teleports that members get are:

Camelot teleport (level 45)
Ardougne teleport (level 51, Plague City quest required)
Watchtower teleport (level 58, Watch Tower quest required)
Trollheim teleport (level 61, Eadgar's Ruse quest required)
Ape Atoll teleport (level 64, Recipe for Disaster subquest for Awowowei required)

After completion of the Desert Treasure quest members can also use Ancient Magick teleports:

Paddewa (level 54): Edgeville Dungeon
Sennistan (level 60): Digsite southeast of Varrock
Kharyrll (level 66): Canifis pub
Lassar (level 72): Top of Ice Mountain north of Falador
Dareeyak (level 78): Level 23 Wilderness west of the Bandit Camp
Carrallangar (level 84): Level 19 Wilderness at the Graveyard of Shadows
Annakarl (level 90): Level 47 Wilderness at the Demonic Ruins
Ghorrock (level 96): Level 45 Wilderness at the Ice Plateau

Enchanted Jewelery Teleports

These are only available to members.

Games necklace: enchanted sapphire necklace, will teleport the player to the Burthorpe Games Room.
Ring of Duelling: enchanted emerald ring, will teleport the player to either the Dueling Arena in Al Kharid or the Castle Wars minigame lobby.
Ring of Life: enchanted diamond ring, will teleport the player to their respawn point if their hitpoints fall below 10%.
Glory Amulet: enchanted dragonstone amulet, will teleport the player to Edgeville Dungeon, Karamja (next to Lathas's plantation), Al Kharid (the palace), or Draynor Village.

Quest Teleport Items

These are all members only.

Camulet: Enakhra's Lament quest required, teleports player to Enakhra's temple, which is close to the Ancient Magick pyramid. Can be recharged by using a bucket of camel dung on it.
Ectophial: Ghosts Ahoy quest, teleports player to the Ectofuntus in far northeast Morytania. Can be recharged by using it on the Ectofuntus
Elf Crystal: Mourning's End Part1 quest required, teleports player to Lletya in the Elven Lands. Can be recharged for a fee by Elenud.
Enchanted Lyre: The Fremennik Trials quest required, teleports player to the entrance of the Fremennik city in Relekka. Can be recharged by offering a shark, sea turtle, or manta ray to the Fossigrimen.
Sled: Troll Romance quest required, brings player down a mountain. Chaos runes and additional sleds can be picked up along the way.

Miscellanious Travel Methods

Besides walking and teleporting, there are various other methods of transportation available to RuneScape players.

Magic Carpets

These can be used in the Kharidian Desert outside of the Shantay Pass. They are a handy way for players to avoid desert animals and to get through the desert more quickly without needing so much water. Players are advised to note that carpet rides cost money and to bring around 500-1000 gp into the desert for travelling costs.

Travel Routes (all routes are 2-way):

Shantay Pass - North of Pollnivneach
Shantay Pass - Ruins of Uzer: requires The Golem quest to use.
Shantay Pass - Bedabin Camp: requires The Tourist Trap quest to use.
Shantay Pass - Nardah
South of Pollnivneach - Menaphos
South of Pollnivneach - Sophanem
South of Pollnivneach - Nardah

Canoes

These are members only.

There are four locations on the river Lum where canoe trees can be found, players can chop these trees to make one of four types of canoe. The canoe can then be used to travel to a different station along the river. Only Waka canoes can travel to the Wilderness.

Stations:

Lumbridge
Champion's Guild
Edgeville
Level 35 Wilderness (Waka canoe only, 1-way so no return trip)

Canoe types:

Log (level 12 woodcutting, can travel 1 station)
Dugout (level 27 woodcutting, can travel 2 stations)
Stable Dugout (level 42 woodcutting, can travel 3 stations)
Waka (level 57 woodcutting, can travel to the Wilderness)

Boat Rides

The following boat rides are available to free players:

Port Sarim - Karamja: 2-way. Costs 30 gp.
Port Sarim - Crandor Island: 1-way. Used once during the Dragon Slayer quest, the trip is no longer available after the player has finished the quest.

These boat rides are available to members only:

East Ardougne - Brimhaven: 2-way. Costs 30 gp.
Port Sarim - Entrana: 2-way. Players cannot bring any armor or weapons to Entrana.
Fishing Platform: 2-way. Sea Slug Quest required.
Waterbirth Island - Relekka: 2-way. Costs 1000 gp for players who have not done The Fremennik Trials quest.
Keldagrim Mines: 2-way ferry. Costs 2 gp.

Magical Portals and Lever

The Magic Guild in Yanille has the following 3 portals:

East - Wizard's Tower by Draynor Village
South - Dark Wizard's Tower north of the Crafting Guild
West - Thormac the Sorcerer's Tower southwest of Seer's Village

In a shack located northwest of King Lathas's castle in East Ardougne, there is a magical lever. This lever is 2-way and goes between the shack and the Deserted Keep in level 55 Wilderness. A knife or a weapon with a slash attack is needed to get out of the Deserted Keep area. Players are strongly advised never to use this lever to get into the Wilderness as it is a pking hotspot.

Quest Related Methods

These are member's only.

Gnome Gliders: Unlocked by The Grand Tree quest. Any glider except the one at the Digsite can take players to the Grand Tree location and from there players can travel to all the other locations. Players can go from the Grand Tree to the Digsite but not the other way around. The gliders do not cost any money to use and they are located at:

1. Ta Quir Priw - The Grand Tree

2. Lemantolly Undri - Western Feldip Hills (requires One Small Favour)

3. Gandius - Just South of the Ship Yard on eastern Karamja

4. Kar-Hewo - Al Kharid palace

5. Lemanto Andra - West of the Digsite

6. Sindarpos - White Wolf Mountain

7. Crash Island - Route to Ape Atoll (requires Monkey Madness)

Mine Carts: Unlocked by The Giant Dwarf quest. Players can travel from Keldagrim to either White Wolf Mountain (Fishing Contest quest required, costs 100 gp) or the Dwarven Mines under Ice Mountain (costs 150 gp). Either White Wolf or Ice Mountain can take the player back to Keldagrim.

Shilo Village Cart: Unlocked by the Shilo Village quest. The cart travels between Brimhaven and Shilo Village. A small fee must be paid, the amount is based on how much money the player is carrying at the moment with the minimum payment being 10 gp.

Shilo Village Boat Ride: Unlocked by the Shilo Village quest. For 25 gp, players can travel from Cairn Isle to Port Khazard or Port Sarim. The trip is one way.

Fremennik Boat Ride: Unlocked by The Fremennik Trials quest. Players can talk to the sailor on the docks of the Fremennik city in Relekka to travel to the islands of Miscellania and Etceteria.

Mort Myre Swamp Boat Ride: Unlocked by the In Search of the Myreque quest. The trip goes from the middle of Mort Myre Swamp to eastern Mort'ton. The trip from the swamp to Mort'ton is free, the return ride costs 10 gp.