How should I know which application is running in 64-bits and which is running in 32-bits in Snow Leopard?
Activity Monitor shows what kind of process is running under the "Kind" column. "Intel (64 bit)" is 64-bit and "Intel" is 32-bit.
To find the Activity Monitor referenced by hanleyp, go to your "Applications" folder and open the folder called "Utilities". Once you launch Activity Monitor look for the "kind" column that hanleyp referenced on the far right hand side of the window.