Where I grew up, the street names were excavated mostly out of a pool of the heroes of the currently ruling ideology; as a consequence, there was no system to it, in the sense there was no sense of direction. Compare to the popular American system of "1st street, 2nd street ... 128th street..." -- you always know how to get from here to there.
In San Francisco they named street in one part of the city in an alphabetical order. So goes like
all the way down to Vicente and Wawona.
Another popular schema is to name a bulk of streets after American Presidents. To provide a sense of direction they have to be named in chronological order, of course, and I don't know if there is a city that implements this or not.
Yet another variant is geographical. The part of San Francisco which doesn't implement alphabetic order, implements geo order (sort of). In one direction streets go like this:
and in another:
Neither axis as it is is particularly instructive, but with some improvements they could be.
Washington DC has a very simple system. North/south streets are numbered, so Sixth street is about six blocks from the Capitol Building.
East/west streets are named initially with letters, B, C, D, etc. I don't know if there is an A street, and I know there is no J (jay) street because one of the guys laying out the names hated John Jay (one of the founding fathers). Once you run out of letters, there are single syllable words starting with A, B, C, then two syllable words Abbot, Barnard, .... then three syllables starting with A, B,
Then there are diagonal streets, they are named after states, nearly always "Avenue". So 1600 Pennsylvania Avenue is a diagonal street, and 1600 is at the corner of 16th street, about 16 blocks from the Capitol.
Its really easy, except that there are four copies of every street/letter, in the four quadrants of the city. So ther eis a 16th and Pennsylvania Avenue North West, and another 16th St and Pennslyvanie Avenue South East.
You can never get lost.
Of course, if you try to knock on the door at 1600 Pennsylvania Avenue NW, you will be arrested, since a guy named Barack lives there
Alphabetical schemes are common in the US. My sister and her family live in a city with streets names Aspen, Birch, Cherry... but then they went with Dale (wtf?), then Elm (back on track), then Fine (another wtf?) and then Hunt - which was apparently an admission that they just couldn't sustain a naming scheme based on trees, nor even a scheme based on the alphabet. Oh well.
In small towns of northern California (by which I mean, well north of San Francisco) it's not uncommon to find streets named simply after letters, e.g. A, B, C, etc. Orthogonal to these, you find streets named only with numbers: 1st Street, 2nd Street, etc. I refer to these towns as Battleship towns. "Where do you live?" "E-7" "You sunk my battleship!" (Martha: this is based off an old commercial, from long before you arrived, sorry.) This naming scheme can also be found elsewhere, but it seems particularly common in this area. Like they weren't even trying to think of new names at this point.
In other towns and cities, I've seen groups of streets named after US states, universities, presidents, cities, counties, countries, native American tribes, local politicians, poets, Catholic saints, trees, minerals, colors (in Spanish), Star Trek references, Beatles songs, and more. OK, the last two were not seen by me directly, but were pointed out in Mapquest or Google Earth. Heck, just start browsing random cities and towns in Google Earth, and I'm sure you can ind some other naming schemes.
Also, in college, I once lived at the corner of 1st Avenue and 1st Street. Very easy to locate - for anyone, unfortunately. Including many drunken students on Friday and Saturday nights, who had heard there was a party at First and First. (Which was true, but we weren't quite planning such a big party.) Fun times.
PF: Of course, if you try to knock on the door at 1600 Pennsylvania Avenue NW, you will be arrested, since a guy named Barack lives there
This reminds me... The next day after Barack inauguration I was on Bush street and wondered if it will be renamed. Then I read in a local newspaper that in fact the street was renamed.
The night of the inauguration pranksters decided to go through the entire length of Bush Street from the Financial district through the Presidio and apply stickers on all of the corner signs reading Bush changing them to Obama.