Heimerdinger, The Fortress of Doom

Fun Fact; Heimerdinger can be a tank, and a deadly one at that.

Heimerdinger can reach 308.71 Health Regen from just 4 items at level 18.

With the right build and runes (at level 18), here's his stats:

3762.59 HP

233.47 - 308.71 Health Regen (40.8 base + 300% from items = 163.2 base health regen, +32.64 from Spirit Visage = 195.84, +37.62 - 112.87 from Warmog's Armor)

180 Armor (plus a stasis)

145 Magic Resist (plus a spell shield)

500+ AP (with Elixir of Sorcery)

Item Build:

Start with Zhonyas for both offensive and defensive power. If you are ahead, get another Needlessly Large Rod to build into Deathcap. You'll want your damage first so you can farm for the rest of the items without any issues. Other than Elixir of Sorcery, these will be your two damage items that you'll need.

After you got your two damage items, you can start building into the rest in whatever way would fit against the team you face. You'll most likely want to get Raptor's Cloak (which build's into Zz'rot Portal) so you can have the movement speed to get back to lane faster, especially if you're up against an AD. The armor will help a lot. By the 2nd defensive item, Heimer will be hard to kill, yet will still be doing plenty of damage.
By the 3rd defensive item, Heimer will be very hard to kill.

If you want to see what I mean, look at this test-match where I got everything I needed other than a finish Warmog's, ending with a winning score of 10/1/12 and getting an S+ ranking: http://matchhistory.na.leagueoflegends.com/en/#match-details/NA1/1819320563/201621485?tab=overview

Runes: Flat AP Quints Mpen Reds Scaling Health Yellows Scaling AP Blues

Masteries: 21/9/0

The movement speed will be low without boots, but you don't really need to move around in battle too much when you build this way. You really don't. Besides, you'll have some help from Zz'Rot Portal when you need to travel. You'll also have Teleport, so unless you are moving through jungles, you'll be fine with getting around.

Overall, this build is rather fun. With Heimerdinger's synergy with Flash and Teleport, boots aren't at all a necessity a lot of the time. As long as you are good at zoning and positioning, you'll be fine.

While it obviously shouldn't be done in every game, I've found this works the best when your team either needs a tank yet no one went one or if the enemy team is filled with tanks, themselves. The build works because most of Heimer's damage comes from early/mid game, where in late game he usually falls off. The build is meant to compensate that weakness by prioritizing a rather hidden strength.