As daveh75 says, mains cables should be kept a minimum of 2" away from non-mains cables to avoid inductance (a mains cable running alongside an HDMI for any distance can generate considerable interference, although that also depends on the construction/shielding of each of the cables too). There are other IEE regs that apply too when routing mains cables in walls - not running them diagonally for example (I can't tell you how many times I've seen that done by keen DIYers!).
On installations I've done when chasing/plastering HC cables into walls, it really depends on the length of the cable run - bundling short runs of non-mains cables together is generally okay and interference free... the longer the run, the increased likelyhood of trouble. But always keep the mains cables well away, and where possible not running closely and in parallel with signal/speaker cables: I know that in practice that's easier said than done, but IMHO it's worth the extra effort.