I remember the first month I played minecraft way back in beta 1.2_01
I liked the sounds more than I do the new ones (not just mobs/ambience, but all sounds). The new ones sound more realistic, but the old ones were awesome and classic, especially the doors. Back then I was scared by hostile mobs, but now I only jump when im going about my business and someone from an enemy faction in full prot IV ninja attacks me.
About the mob noises... the easiest would be getting a mod or editing/replacing the sound files with blank ones (they must be the same exact length), or playing other music in the background, like suggested above
You could also make a mob farm and get used to the sounds, or join a hardcore factions server (mobs will be nothing anymore once you get used to pvp)