How many items can produce light?

There is a list of light-emitting blocks on the Minecraft Wiki.

These blocks along with the light levels the produce are as follows:

• Fire - 15
• Jack-O-Lantern - 15
• Lava - 15
• Glowstone - 15
• End Portal Block - 15
• End Gateway Block - 15
• Active Redstone Lamp - 15
• Beacon - 15
• Sea Lantern - 15
• Torch - 14
• End Rod - 14
• Lit Furnace - 13
• Nether Portal Block - 11
• Redstone Ore, when touched - 9
• Active Redstone Repeater- 9
• Ender Chest - 7
• Lit Redstone Torch - 7
• Magma Block - 3
• Brown Mushroom - 1
• Brewing Stand - 1
• Dragon Egg - 1
• End Portal Frame - 1

While not technically blocks, additional light sources include:

• Sunlight - 15
• Sunlight when raining or snowing - 12
• Sunlight, when thundering - 10
• Moonlight - 4

Additionally:

Certain blocks will only allow light to pass through diffusely. These are water and ice, which reduce light by an additional 2 levels per block, and leaves and cobwebs, which diffuse sunlight but only reduce light by the normal 1 level per block.

There are also quite a few lighting bugs to consider.

In the new Aquatic Update, sea pickle also produced light from 6-15 (only if waterlogged) depend on how much pickle are there.