Can creatures follow me through a portal?

Can creatures from both the Nether and the Overworld follow me through a portal? Is it safe to build a portal in the open, or should it be surrounded in a cobblestone hut to prevent unwanted travellers?

Can regular creatures use the portal to enter the Nether, or can I use it to evade them?

Solution 1:

Note: This answer applies to Minecraft 1.4.1 and earlier. For newer versions see the other answers.

Mobs can not follow you through a portal. "Follow" meaning continuing a pursuit by entering the portal after you do and chasing you again once you're on the other side.

Currently, the only danger coming from the existence of a portal is the possibility of a Ghast spawning by it in the "Earth", "Overworld" or whatever we now call the main area of the game. The space they need to spawn there is at least 4x4x4 and, according to Notch, their appearance near the portal is "extremely uncommon".

Solution 2:

As of Minecraft dev version 1.4.2, mobs have the ability to travel through portals. Taken from the wiki:

• Added new Full-screen toggle to the Video settings.
• Added new use Vsync toggle in the Video settings.
• Improved maps
• Maps now align to a grid, making it easier to create adjacent maps.
• A compass and paper do now create an empty map
• An empty map has no data on it until you right click on it. The point on your world - - - where you right clicked it is the map's center
• A map (with data) can be cloned. Cloned maps are stackable
• Maps can be zoomed out (but not zoomed in)
• Stairs now auto-arrange into corners. This is a test and may change based on feedback.
• Mobs (and all other entities) can travel through portals.
• Fire charges shot from a dispenser or a Blaze create the "fireball" sound effect. Leather armor can be dyed.

Thus to answer your questions above:

Can creatures from the Nether come through a portal?

Yes, they can. This now applies to all mob entities, including the Wither and Enderdragon bosses.

Is it safe to build a portal in the open, or should it be surrounded in a cobblestone hut to prevent unwanted travelers?

Depends on how you are playing your game (ie game difficulty)

Can regular creatures use the portal to enter the Nether, or can I use it to evade them?

You will not be able to travel through the portal instantaneously, but mobs can. Also, the player now can go through the nether quicker, as of 12w38a. As for mob behavior, they do not chase you into the portals. They may wander into the portals, but not by following the player.