The short answer is, it depends. The long answer is, try reading through the wiki page. The medium answer, then, is perhaps the most interesting…
The radius of an explosion is dependent on three main factors: the "power" of the explosion, the explosion "resistance" of the materials being destroyed, and a random factor.
Explosion power is 4 (approximately four blocks) for TNT, 3 for uncharged creepers, 6 for charged creepers, just 1 for ghast fireballs, and 5 for nether beds. Block resistance varies wildly, from 0 for air and weak blocks like redstone wiring, to 30 for most types of stone, to 18,000,000 for bedrock!
When an explosion occurs, it sends out a large number of invisible "rays", each with 70%-130% of the explosion's power. When a ray strikes a block, it's power is applied to the block's resistance. If the power is higher, the block is destroyed and the weakened ray travels on. If the resistance is higher, the ray is stopped, but the block is weakened against other rays.
The upshot of this is that explosions travel to a maximum of 1.3 times their power in blocks, through air. So airburst TNT will reach about 5.2 blocks from its center. Through solid stone, however, TNT will only carve out a single block on all sides (a radius more than one, but less than two).