Are people allowed to trademark an arbitrary letter of an arbitrary alphabet? How about arbitrary collections of letters that may or may not form a 'word'?
Yes and yes. "IBM" doesn't form a word, but it's a perfectly valid trademark and you would be sued into oblivion (quite fairly at that) for trying to sell computer software or hardware as "IBM." Gatorade has a trademark on a capital "G" in the field of sports drinks because consumers have come to recognize the "G" line of products. "Google" is a mostly-made-up word (it was at least unfamiliar before Google became popular) and it is a valid trademark. "Apple" is a commonly known word and it is also a valid trademark. The symbol for Prince [1] is an arbitrary symbol that could also be trademarked.
The key fact is that trademarks protect the right to use a word or symbol in connection with selling goods or services in a certain field. Apple doesn't get to ban all uses of the word "apple" but you couldn't go sell your own products as "Apple Computing Stuff". Prince can't ban people drawing the symbol linked above, but he could sue anybody who released a CD with that as their cover artwork. Gatorade doesn't control all uses of the letter "G" but I wouldn't try selling a sports drink with just a capital G on the bottle.
Zazzle done messed up, but not because letters or symbols alone couldn't be trademark.
The key fact is that trademarks protect the right to use a word or symbol in connection with selling goods or services in a certain field. Apple doesn't get to ban all uses of the word "apple" but you couldn't go sell your own products as "Apple Computing Stuff". Prince can't ban people drawing the symbol linked above, but he could sue anybody who released a CD with that as their cover artwork. Gatorade doesn't control all uses of the letter "G" but I wouldn't try selling a sports drink with just a capital G on the bottle.
Zazzle done messed up, but not because letters or symbols alone couldn't be trademark.
[1] http://en.wikipedia.org/wiki/File:Prince_logo.svg