How is having only six skill slots negatively impacting your gameplay experience right now? If you can cite specific examples, even better!
Let us say, for example, that I am playing the Witch Doctor. Basically the only skill that is reliably going to save me from the "OH !@#$ VORTEX!!" moments is Spirit Walk. Otherwise I have to accept the fact that I will die 2-3 times against Vortex, area denial or Waller/Jailer enemies. In case of Champion packs who can chain-vortex/wall/jail me, having an escape ability with a 15 second cooldown means I can reliably escape the first Vortex, I can maybe walk out with some health from the second one and I die to the third. If I want to avoid these (regular and commonplace) situations, I have to have another defensive skill to hold me over when my Spirit Walk is on cooldown. I also naturally have to have a primary skill.
That is three slots occupied by mandatory skills, leaving me with 3 that actually define and differentiate my build from the others. 1 will most likely be a massive DPS skill for those dangerous monsters you simply cannot be killing over time. Those who have to die NOW, like armodons. Ok, 2 slots left. AoE is a must and many heavy nuke abilities don't have much AoE (Hammer of the Ancients for example). Ok, 1 slot left. This is the slot you can put something fun into. The others are mostly set for you.
Primary - Firebomb
AoE: Zombie Bears;
Fun: Zombie Dogs.
Now if I want to maximize the use I get from Zombie Handler passive, I would like to take Gargantuan, but Gargantuan isn't very defensive, is on long cooldown and wont help me in jail or vortex situations. I am left with the choice of making a fun summoner and dying all the time, or going safe with two defensive skills and having no fun with the build.
On the flip side, how would having an extra skill slot improve your game experience?
Having an extra skill slot would remove the frustration of having to occupy 2-3 slots with mandatory skills that are necessary for survival but aren't essentially a part of YOUR BUILD. If you want to make a Summoner WD, having something like spirit walk isn't THE BUILD, it is what you need to even stay alive to play your build. The basic frustration isn't created by the fact that there are too few slots, but by the fact that you need very specific must-have skills to deal with artificially created danger situations such as getting Vortexed/Chain-Frozen/Walled/Jailed. This is further amplified by base monster abilities such as Deceiver's invisibility, Phase Beast's teleport, Lasher's tongue grab, Armodon's stun etc.
If you had a 7th skill slot, what additional spells or abilities would you add to your bar (on top of the builds you use currently)?
I would use skills that complete my build, give it a fun factor, have long cooldowns or simply make more use of my passives. If I take the No Escape passive, it's almost a wasted passive slot if I'm not using both Weapon Throw and Ancient Spear. If I'm using both, I'm creating giant holes in the character. If I'm wanting to make a Fetish WD, and make as much use as I can of Tribal Rites, I can use Hex, Big Bad Voodoo and Fetish Army (no clue why they replace my Sycophants :-/) a nuke and a primary for Sycophants and a single defensive skill, but I have occupied 3 of my slots with fun skills and my survival needs have gone to hell. If I take survival over some of the fun skills, my Tribal Rites almost feels useless because it only decreases a cooldown of a skill or two.