I always thought this and i applied for my first industry job with a game demo and some tech demos built on a moderately over engineered engine, and my second one with a fps demo with most standard last gen (360/PS3) lighting features and support for real world data formats (quake 2/3 bsp, md2, obj, 3ds, lwo, png, tga, jpg etc.) and a tools pipeline involving radiant and the appropriate game bsp compilers to create levels.
sadly most people i have worked with have made no serious demos or games in their spare time and this is much less common than i had imagined.
knowledge about things like rendering, audio, AI, networking is rarer and will help - however a gameplay programmer is a thing - although despite it seeming like a super generic role there is a skill to creating good and flexible gameplay systems for designers, or in picking the right hacky function to make something 'feel' 'fun'.
oh and be prepared for low pay on the way in - you don't have to tolerate it but i've heard salaries ranging from /actually very illegal/ to £20k for new juniors. i took £17k for my first - if i had known better - and esp the pay rates of my compatriots then i would have asked for more from the beginning...
also try agencies if you don't know many games companies.. you will never be able to rid them from your life and they will do stupid things like call you at your current job and speak to your boss when they can't get through to your personal phone - but its their job to find you something or be honest if they think its not possible.