Abbreviations are a good source of pleonasms. Unfortunately, these aren't the kind that make you sound literary, these are the kind that make you sound dumb to people who know better. Here are some examples of common gaffes:

ATM machine
Automatic Teller Machine machine
PIN number
Personal Identification Number number
CAD design
Computer Aided Design design
SCUBA gear
Self-Contained Underwater Breathing Apparatus gear
ISBN number
International Standard Book Number number
LCD display
Liquid Crystal Display display
MIDI interface
Musical Instrument Digital Interface interface
GUI interface1
Graphical User Interface interface

There are also a number of borderline pleonasms that come up when foreign language words get transplanted. Since the meanings of the words are not generally know to the users, it's debatable at to whether they're really redundant. Here are some examples of this:

minestrone soup
soup soup
Rio Grande river
river big river
The La Brea Tar Pits
the the tar tar pits
Sahara desert
desert desert
Mount Fujiyama
mount fuji mountain

Of course, there are other redundant pleonasms, but when you yourself are writing in a literary context or participating in spoken discourse it can be impossibly difficult to say whether you are attempting to try for strengthened emphasis, or if you're just a stupid idiot.

  1. I actually got called on this one while making a presentation about a program I had written. I felt very stupid.