Funny, I actually found that New Vegas had far more opportunities to be a truly heartless bastard than any of the Elder Scrolls games heh.
Being truly evil in Skyrim can be somewhat underwhelming, depends on what brand of evil you'd like to be. Most of the Daedric quests are a must, since you do some pretty horrible stuff in them. If you've got Dawnguard, you can join the vampires after the first couple of quests in that, easily one of the most overtly evil things you can do in the game. You automatically get a very plot-relevant follower in the majority of Dawnguard's questline, too.
As for Shouts, http://www.uesp.net/wiki/Skyrim:Dragon_Shouts#Available_Dragon_Shouts. One in particular, also from Dawnguard, is Soul Tear, which is just about the most malicious one there is. Does a solid amount of damage, soul traps the target, and immediately resurrects them as your undead thrall if the Shout is the kill shot. There are a few others that can be easily seen as evil, like Marked for Death, Dismay, and Drain Vitality.
For a lot of quests, though, your evil choices will be through your character's motivation in your head and won't show in the game itself, unfortunately. For example, in the Dragonborn DLC (I'll try to avoid spoilers as best I can), someone sends a couple assassins after you. When you confront the person, you can easily make it a simple revenge trip for daring to threaten your personal power, and saving the citizens of Solstheim is merely a coincidental side effect of having your vengeance.
Hope that helped a bit, at least!