Low Serial Numbers

Serial numbers that start with four or more zeros are fancy: meaning 00000001 - 00009999.  The more leading zeros, the better.

High Serial Numbers

Serial numbers that start with four or more nines are fancy: meaning 99990000 - 99999999.  The higher, the better.  All notes are printed starting with serial number 1, but recently notes have NOT been printed to 99999999.  Notes printed on sheets of 32 and 50 within the past few decades (uncut sheets excluded) are only printed to 96000000.  Prior to that, block letters have rolled over at various increments - 99200000, 99840000, and 99999999.

For a recent note that has a block rollover at 96000000, you might think "that means 95999173 is rare because it's within 827 of the highest number, similar to five leading zeros."  Maybe a collector might find it interesting to pay over face value for, but I think it would be considerably lower than a five leading zero number.

Ladder

Each digit is one number higher or lower than the previous digit. Examples: 01234567, 98765432. Some people consider ladders fancy if they go up and down like: 23456765, or wrap around from zero: 56789012.

Binary

Binary serial numbers contain only two unique digits (order doesn't matter). Example: 74774774

True Binary

True binary serial numbers are a kind of binary that contain only zeros and ones - like machine code. Example: 01001101

Trinary

Trinary serial numbers are like binaries, except that they contain only three unique digits.  Again, order doesn't matter. Example: 79557977

Repeater

The first half and second half of the serial number are the same. Examples: 74627462

Super Repeater

A super repeater is when the first two digits are repeated four times. Example: 39393939.

Quad Double

In a quad double, the first four digits are the same number, and the last four digits are the same number. Examples: 55553333, 11116666

Radar

Radar serial numbers are the same forward as it is backwards. It is named this because the word "r-a-d-a-r" is spelled the same forward and back. Examples: 12533521, 49366394

There are also more types of radars:

Repeater Radar
The radar is also a repeater, meaning the first four digits and last four digits are the same as well as the entire number being the same forwards and backwards. These types of radars are inherently also binary. Examples: 34433443, 61166116

Binary Radar
The radar only consists of two digits. Examples: 83833838

Solid

Every digit in the number is the same. Examples: 11111111, 88888888

7-In-A-Row

Seven of the same digit are in a row. Example: 77777771

7-Of-A-Kind

Similar to 7-in-a-row except that the lone digit is somewhere in the middle of the number. Example: 77177777

Date/Birthday

Serial numbers can contain dates. The format might change depending on your locale, but a number like 07041776 or 02221732 could indicate the finalization of the Declaration of Independence, or George Washington's birthday. Some people try to collect numbers matching their birthdays or other life milestones.