Let's just be up front about this now -- the Titans left stuff everywhere. It would be hard to disbelieve in them, frankly. They left bases, research stations, fortresses, labs and more. We don't even know what everything they left behind originally did or why it was there in many cases. Some places have somewhat clear reasons for existing (Ulduar, for instance, was tasked with holding the Old God Yogg Saron prisoner, but the Halls of Stone and Lightning point to other goals for the complex) but others, such as the ruined complex now known as Ahn'Qiraj was simply a 'research facility', and we have no idea what it was researching or why such a complex was needed so close to Uldum.
At any rate, there are a lot of Titan complexes currently known of on Azeroth.
Northrend has several Titan complexes and ruins. For starters, there's the aforementioned Ulduar, with the Halls of Stone and Lightning as well as the massive main complex. Several other Titan structures dot the entirety of the Storm Peaks, all undoubtedly related to Ulduar in some fashion. (For instance, Mimiron has a workshop and a library in the Storm Peaks and many parts of the Forge of Wills extend throughout the entirety of the Storm Peaks. The Titanic Watchers or Keepers also have temples dedicated to themselves in the zone.)
In addition, there are several Titan terraces in Sholozar Basin (as well as a Titan waygate usable to travel to Un'goro), further Titan structures in what is now called the Strand of the Ancients and Wintergrasp (the Vault of Archavon within Wintergrasp Fortress) and Azjol-Nerub itself was formerly a Titan complex as well. (The Obsidian Destroyers used by Scourge forces in Warcraft III were once Tol'vir from this Titan base.) In addition to all of these Titan structures, the Wyrmrest Temple in the Dragonblight (linked to Ulduar by the ancient Path of the Titans highway, which presumably continued south to other Titan bases. It's also possible (but not definitively stated) that the Titans were responsible for the creation of the Nexus, but that could simply have been the blue dragonflight at work.
There was also a mechagnome buried in parts beneath the Borean Tundra, Gearmaster Mechazod. He was capable of removing the Curse of Flesh from gnomes at the very least. Whether there's a lost Titan base there or the Nexus/Eye of Eternity was once a Titan base is unknown.
Northrend's extremely high amount of Titan facilities seems based around two goals. The Ulduar complexes seemed to originally be based around creating various constructs (there's a Titan creation forge, the Forge of Wills inside Halls of Stone, and a stockpile of Iron Vrykul inside the Halls of Lightning) before being re-purposed to serve as a prison for Yogg-Saron. The other Titan complexes in Northrend seem based around the Titan's goal to shape the entire world, from the Sholozar Basin lab experiments (the petri dish of the Titans, so to speak) to the Wintergrasp and Strand of the Ancients Titan relics and the Wyrmrest Temple. Whether or not the Path of the Titans was considered part of either, or both, or an even larger purpose (since it seems to have originally linked all Titan facilities together) is also unknown. We also don't know what the Titan complex-city that became Azjol-Nerub was for, although since it had tol'vir stationed there it may have been an information repository. Since it's clear that there was a lot of research going on, that would make sense, and Azjol-Nerub is fairly well central in the Dragonblight between Wintergrasp, Wyrmrest, Sholozar and Storm Peaks.
There are also some form of ruins being excavated by the Explorer's League and then attacked by iron dwarves under the command of Loken in the Howling Fjord.
Races of Titan origin found in Northrend include the vrykul, earthen, giants of various kinds, mecha-gnomes and iron dwarves. The Titan Keepers or Watchers have a heavy presence in Northrend, with Loken (the Prime Designate) operating out of the Halls of Lightning (and being corrupted by Yogg-Saron) and Thorim, Mimiron, Freya and Hodir within Ulduar itself. Also Jotun, the Titan Watcher known as the Curse Bearer, walks the Path of the Titans in the Dragonblight.
The Eastern Kingdoms appears relatively sparse in terms of Titan facilities in comparison with Northrend or Kalimdor. Indeed, the only real facility of any note in the Eastern Kingdoms is Uldaman. However, the bit of Uldaman that we can actually access is just a small fraction of the original installation. As indicated by the map chamber, there was once a far larger full fledged Titan city above the mountains of the Khaz Modan region, perhaps even predating their creation.
We know fairly little about Uldaman's purpose. Clearly, it had many early earthen prototypes within it, which suffered matrix destablization from the Curse of Flesh (the curse used by the Old Gods to corrupt the creations of the Titans, turning them into flesh and blood beings which are easier for the Old Gods to assimilate) and became both modern dwarves and troggs. There must also have been a colony of mechagnomes in the region as well, as modern gnomes are descended from them via the Curse of Flesh as well. It's feasible that Gnomeregan is built around a core of ancient Titan technology, but if so, the modern gnomes seem fairly disinterested in it.
Whatever the Uldaman base was originally intended to do (neither Archaedas nor Ironaya speak of it when engaged, although Ironaya is apparently attempting to repair the facility) it clearly held a great many earthen. Since all current dwarves of the Bronzebeard, Dark Iron and Wildhammer clans can trace their descent to earthen released from Uldaman and because there are still a great many earthen within the complex, their original numvers would have had to be vast. (Granted, modern dwarves can reproduce more readily than earthen, who require a creation forge such as the Forge of Wills.) Factoring in the presence of nearby Stranglethorn Vale, with its raptors and hints of Old God corruption, and one wonders if Stranglethorn was originally similar in purpose to Un'Goro or Sholozar.
One notes that other regions with dwarf or possibly Titan influence like the Wetlands and Arathi Highlands also have raptors. (Myzrael, clearly a Titan Watcher similar to Ironaya, was imprisoned in the Arathi Highlands after being corrupted by the Old Gods, eventually managing to return to the Titan created temple in Deepholm after being cleansed.) It's possible an ancient Titan vault of some kind resides deep below the surface of the Arathi Highlands, or perhaps reaching as far as the Tirisfal Glades.
Kalimdor contains a great many Titan complexes and ruins, second only to Northrend (and in part that may be due to the distribution of some of its complexes to Pandaria when the two continents were parted). The Titan vault in Terramok (known known as Maraudon) is of unknown purpose, although apparently it imprisoned Princess Theradras at one point in time. When he tried to enlist her aid Cho'gall mentioned that Theradras was 'no longer bound to this prison' but she insisted it was now her home. Terramok is full of crystals similar to those used elsewhere in Titan technology.
However, it's the massive Uldum complex and its former satellites (now known as Ahn'Qiraj) that are the largest and most impressive Titan constructions on Kalimdor. Uldum contains the Halls of Origination, a massive engine whose power could if activated utterly shatter and remake Azeroth entirely. While Ulduar apparently contained the platform for the determination of the need for planetary reorigination, it was Uldum which would accomplish that feat, and the enormous Titan structures throughout the region all seem designed to feed power to the Origination engine. It is potentially in Uldum that life as we know it on Azeroth was first created, tested in the nearby Titan petri dish of Un'Goro - complete with Titan crystal spires and Terraces, as well as the Etymidian, and a waygate to Sholozar.
With Uldum clearly created and designed to support the Origination engine, and Un'Goro a test bed for new biological creations (as was Sholozar to the north) one wonders what purpose the 'research station' we now know as Ahn'Qiraj served. Clearly several tol'vir and Titan Keepers resided her, ultimately corrupted by the Old Gods (Ossirian, the Anubisath like Roman'khan and Setis) just as Uldum possesses its own Anubisath like Setesh. It's possible that Ahn'Qiraj was intended to hold C'thun just as Ulduar served to hold Yogg-Saron - both the chamber the Twin Emperors of the Qiraji reside in and the one C'thun can ultimately be found within are similar in size and scope to the one Yogg-Saron inhabits.
The only relatively common Titan constructed race to be found in Kalimdor are the tol'vir. There were no native dwarves, gnomes or vrykul (or their human descendants) anywhere in Kalimdor following the Sundering. The centaur revere Terramok, but their origin is fairly well known as descending from Theredras (a child of Therazane the Earthmother, an elemental lord) and Zaetar, a keeper of the grove descended from Malorne and Elune. At present no other Titan created races inhabit the complexes of Kalimdor.
Pandaria has its share of Titan complexes, although many of them appear to have been constructed after the departure of the Titans themselves by the mogu, who are a Titan created race. Pandaria contains the Mogu'shan Vaults, built to conceal and house the Engine of Nalak'sha (a Titan creation forge similar to the Forge of Wills in Ulduar) as well as the final resting place of Ra-Den before the coming of Lei Shen. The entire Vale of Eternal Blossoms seems to be intended to be similar to Un'Goro and Sholozar, although the Mogu'shan Palace and the shrines seem to be built along similar lines as the Mogu'shan Vaults, as is the Terrace of Endless Spring in the mountains near the Vale. Since thge mogu themselves were Titan constructs similar to the tol'vir, vrykul and earthen, it's not surprising that their works are Titanic in scale and scope, built as they are on the backs of the Titans.
It seems likely that at one time the Engine of Nalak'sha and Vale of Eternal Blossoms were linked to the Kalimdorian complexes in Un'Goro and Uldum/Ahn'Qiraj in some as yet unknown fashion. The Prophecy of C'thun seems linked to the fate of Y'Shaarj, who 'died' somewhere in what is now Pandaria, but long before the Sundering and the mists separated the continents. Looking at the world map, Pandaria was likely in physical contact with both Stranglethorn and Tanaris in those days, placing it fairly close to Uldum. Of course, it's hard to know exactly how the extant lands lined up into the single super-continent of Kalimdor before the Sundering, and how/if the Path of the Titans actually reached to each of them.
The Thunder King's palace on the Isle of Thunder may have been created by the mogu long after the Titans departed, and thus would not count as an actual Titan facility. At present the mogu and the grummles (descended from troggs, and thus cousins to dwarves) are the only Titan created races native to Pandaria.
Whether there are more Titan secrets yet to uncover (did they make any underwater facilities, were there Titan bases on Azeroth's moons) only time will tell.
While you don't need to have played the previous Warcraft games to enjoy World of Warcraft, a little history goes a long way toward making the game a lot more fun. Dig into even more of the lore and history behind the World of Warcraft in WoW Insider's Guide to Warcraft Lore.