This is a reference post. It may be updated.
Mega Prims, Huge Prims, Prims with dimensions greater than 10M.
They're a child of the libsecondlife project. The grid used to not validate object sizes that were passed to them in some cases. That has been fixed, so all existing mega prims are copies of the ones created on the grid before that time. They currently can't be made on the grid.
They can't be resized, but you can twist, hollow, cut, etc. Twists and other modifications may be ignored during collision calculations, making them interesting to interact with. You can change the cubes to cylinders. It has been said that some of the curved mega prims are treated by the physics engine as cuboids. They can be used with sculpted prim textures.
There's conflicting information about hollowing them; some sources claim that they only appear hollow, others claim that they hollow as if they were 10M versions of the shape. I've had no problems hollowing basic ones myself, but I've only worked with the smaller ones.
I have one that hollows strangely - it visually hollows as both a box and a cylinder, but it is phyically hollow only as a cylinder.
There's a trick used to make tiny prims where you dimple a sphere, then convert it to a box. Several of the huge box prims available were created from other huge prims using this technique. Their "center" when you edit them is far away from what you see of the cube, and several of the edit controls seem strange (hollow acts as cut, etc.)
Larger ones can upset the physics engine, causing sim lag and crashes when things collide with them. There's also talk that some of the largest ones can cause a "pull" - avatars nearby find themselves moving toward the prim as if it had its own gravitational force.
Object culling in the viewer can do strange things to them. Culling is based on the prim's center, so if the viewer's distance is short, they might not see the prim. Sim borders and object culling require special consideration. A sim only looks so far into another to find prims, so don't depend on a megaprim to be a bridge across sims.
If you use them, you're advised to not us them as physical or flexi, and to use them as phantom. Respect parcel boundaries, and make sure they aren't intruding on the neighbors.
LL's official statement on them has shifted over time; if you plan to use them keep yourself informed. As of the last edit here, they're allowed on both mainland and island sims. Builds using them that are perceived as "causing sim problems" will be deleted without warning. Requests to remove them entirely from the grid have been refused with the comment that it would break existing content.
Mega Prims are freely available on the grid, and from SLExchange.com
Links to SL Forum threads about mega prims.
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Second Life Insider article about the 2006-2007 mega prim controversy.
Second Life Insider article about megaprims and making a case for unlimited prim sizes.
EDIT: April 2008
With Havok 4, megaprims are now treated as they appear for collisions.