Is there any way to cause lava source blocks to replicate in Minecraft?

Note: This answer exploits an old bug which has been patched in the current version of Minecraft.

No, lava can't replicate, but you can create unlimited obsidian from one lava block using a glitch involving lava flow onto redstone wire:

Not Any More

In Minecraft Beta 1.9 pre-5, you could make infinite quantities of lava by placing 4 lava sources around a central block as so:

As pointed out by Ben Blank, this behavior was scheduled to be reverted, and no longer works.

Both top answers rely on bugs that existed in previous versions of MineCraft, but have since then been fixed.

In the current version (MineCraft 1.7.4), there is no way to get infinite lava source blocks or lava buckets.

However, you can get infinite obsidian by exploiting the fact that portals between the nether and the overworld are re-created (offering "free" obsidian) if no existing portals are in range. This mechanic is described about half way through this video, and still works in 1.7.4: