Here are links to some of the websites I find myself consulting most frequently.
LINKS FOR RESEARCH IN MEDIEVAL HISTORY
Addall.com: the best used-book search on the web, which aggregates results from all the major databases.
HOLLIS: the Harvard library catalogue.
Perseus DIgital Library: major repository of Greek & Latin texts, including dictionaries.
The Latin Library: unlike Perseus, includes a number of late antique and medieval authors.
Dizionario biografico degli italiani: online edition of the most important Italian biographical dictionary (1960-).
Orbis Latinus: online edition of Johann Grässe's 1909 reference work, matching Latin placenames with modern ones.
The Digital MGH: online version of the Monumenta Germaniae Historica, the most important German series of editions of medieval sources (not just German ones).
Documenta Catholica Omnia: PDFs of DuCange's Glossarium (medieval Latin dictionary); Mansi on church councils; Forcellini's Latin dictionary; Muratori's Annali d'Italia; the Acta Sanctorum; and more.
Patrologia Latina: series of 200+ volumes of editions of medieval texts in Latin at Documenta Catholica Omnia (contents of each volume are indexed for separate PDF download). This is most useful if you know what text you need but not what PL volume it appears in, but downloads of full volumes of the Patrologia are also available. I have also found this index to the PL volumes helpful.
Historic Cities: contains high-resolution historic maps for most European towns and cities.
Royalist.info: genealogical website covering most European dynasties from the Middle Ages to the present.
Fordham Medieval Sources Bibliography: bibliography of editions and translations of medieval works available in print and online. Not comprehensive but still helpful, especially when searching for works available in English translation.
XKCD: a webcomic.
PHD: Piled Higher and Deeper, another webcomic.
Academic Coach Taylor: has some advice for you.
Historic LOLs: captioned portraits of yore, from the geniuses/idiots at I Can Has Cheezburger.
Globegenie: uses GoogleEarth to take you instantly to some random place in the world. Last time I ended up in the Shetlands.
Captain Awkward: one of the internet's best advice-column sites. Should be required reading for all college students.
Calming Manatee: Manatees make the stress and badness go away. Recommended for second-semester thesis students.
Luther Insult Generator: All from the collected works of Martin Luther! One favorite: "."
Fontcraft: font-design company with a great range of historical fonts. See also Walden Font, P22, and Crazy Diamond Design. My favorite amateur type designer is Pia Frauss. And while we're at it, here's a great blog post on the rules for using long S in early modern typography.
KernType: a game, for font geeks only.
Pandemic: Be the Black Death! In the Flash game Pandemic, you're a disease trying to kill off the world.