While Mannheim, A major industrial city in southwestern Germany, doesn't go back all that far–its city center was laid out in its present form sometime in the 1700s, if I read the histories correctly (and I may not, in all fairness). The city center itself is press-fit between the Rhein and Neckar (a major river in south-central Germany) and is conspicuously recticlinear.
The first illustration here, Exhibit A, is taken from the Wikipedia entry on Mannheim and is taken from the 4th edtion of Meyers Konversations-Lexikon (Meyer's Encyclopedia), which was published from 1885-1890. The grid, oriented more or less toward the Rhein, is encircled by a horseshoe-shaped ring road, and centers on a building that was then the palace of the Prince-elector (Kürfurst) at the south side of the grid (on this map, it's noted as Schloß, also spelt Schloss (the terminal charcter, ß, is a glyph in the German alphabet which simply reduces to "ss" and is my favorite letter in any alphabet, and we're deep in digression land again) It shows little of the surrounding areas (only a section of the neighboring city of Ludwigshafen (Ludwig's harbor) across the Rhein and the burg of Neckargärten (Neckar gardens) across, appropriately, the Neckar.
The next illustration, Exhibit B, is clipped from a Google Maps display, and gives a sense of surroundings. While straight streets and griddish patters can be found around, there is nothing that has the sense of planning that the city center has; the rest of the area seems uncoordinated in comparison.
The last illustration, Exhibit C, is a closeup of the most detailed online map of Mannheim that I could find (clipped from this page):
Now we get down to interesting cases. Perhaps you've noticed the abscence of one very imporant thing (and it was obvious if you zoomed in on the map in Google): there are next to no street names. The surrounds have names (the ring road is named, at different places, Luisenring, Friedrichsring, Parkring, and Kaiserring (the suffix ring tends to be used for semicircular streets like crescent in the Commonwealth or circle here in the USA) and a few of the grid streets have names as well (the horizontal street that intersects at Stadt Parade Platz is named, from west to east, "Rheinstrasse", "Planken", and "Heidelberger Strasse", and the vertical center street is named "Kürpfalzstrasse", essentially, "Electoral Palace Street"), but, instead of street names, we have what look like a sort of grid coordinate in each block (or Quadrate, as locals call them).
The pattern of Quadrate naming follows a logical sequence with an exception, and this pattern relies on the position of Kürpfalzstrasse as an assumed centerline. The ranks-the horizontal rows–are lettered increasing away from the Bismarckstraße baseline. Ranks on the west side of Kurpfalzstrße are lettered A through K, and ranks on the east side take up the sequence again with L and proceed through U. Files–the vertical columns–number in sequence away from Kurpfalzstaße both east and west. The exception comes with the L rank, which includes a row of blocks south of Bismarckstraße which are numbered in a leapfrog pattern until L14 and L15 at the Bismarckplatz.
My understanding of addresses is somewhat limited here, but if I remember my reading correctly ,it's rather Japanese in manner; your address is a number in the Quadrate your place is located in. For example, if you live in a flat (if such exist) four streets north of Bismarckstr. and three streets east of Kurpfalzstr., then your address is a number in Quadrate O4.
This seems rather innovative for the day, I'd guess. It certainly reinforces the ideal of the German as a lover of efficiency and precision, and, in its regularity and order, stands out as a unique city center plan on the European continent (as least as far as I'm aware).