Scrapper Split Push Build
Ghost is a fair alternative to Flash in some lanes.
Shyvana's greatest strengths are her mobility and 'Are of Effect' damage. To this end, she makes an excellent split pushing champion. She's relatively flexible when it comes to item builds, and can focus on being able to scrap it out with one or two targets (such as in the scrapper build), focus purely on a gate pressure approach (such as in the split push build), or even build exceptionally tanky.
Ninja Tabi: If you're going to be fighting people in extended fights, build these.
Mercury's Treads: If you're worried about CC, particularly on a team-fighting build, pick these up.
Boots of Swiftness: Only pick these up if you're going to focus on a mobility oriented split-push build, or if you're more concerned with slows than auto-attacks.
Berserker's Greaves: Not the best option, but situationally viable when you're in the process of snowballing your lane out of control via a high DPS build. Usually Ninja Tabi are better.
Trinity Force, despite the wasted mana, is an exceptional item on Shyvana. It provides incredible mobility, and unmatched split siege damage.
Blade of the Ruined King is the single strongest damage item on Shyvana. Period.
Titanic Hydra is also an excellent damage item on Shyvana, particularly in a tankier build, or with a team-fight focus. Great against squishy targets.
Dead Man's Plate: Mobility, armor, health, and a slow. Great for starting fights you think you can win, and running away from fights you're not so sure about.
Spirit Visage Excellent magic resist option, especially if your team has dragon control.
Banshee's Veil Budget magic resist option if you have health in other places.
Guardian Angel: If you're going to team fight, it's pretty darn good.
Zz'Rot Portal: If you're not going to team fight, and would rather just open up the gates, it's pretty darn good.
Warmog's Armor: If you're applying pressure, it'll keep you on the map and healthy.
Frozen Mallet: Much better on Jungle Shyvana, but in a lane build, it's great for catching people if your team is playing up.
Thornmail: Combined with health items, this is your counter to being hit a lot. Combine with Ninja Tabi if possible.
Randuin's Omen: If you're fighting the AD carry, and it's not a caster, build this.
Maw of Malmortius: In a damage heavy build, this is a solid buy. Especially useful if a Hexdrinker would do you good in lane.
Wit's End: A bit of a dated Shyvana item, but still quite decent in certain cases, particularly as a DPS item on a tankier build.
Sunfire Cape If you're building Tank, this is your 'Win-Lane' item.
Locket of the Iron Solari: If you're building tank and fighting with your team, this might be a good situational pickup.
More on the Tank build.
Sunfire Cape + Ninja Tabi is your win-lane button vs AD.
Spectre's Cowl + Wit's End or Titanic Hydra is your win-lane button vs AP.
Don't look to build more damage than Wit's End and Titanic Hydra.
Maxing E second is your friend here.
Health is your friend here.
Fury, Feast, Natural Talent, Battle Trance
Recovery, Explorer, Runic Armor, Insight, Swiftness (or Legendary Guardian), Grasp of the Undying