I would write URLs, and not URL's, but I can understand why somebody would write URL's.
The NOAD reports that 's us also used to denote the plural of letters or symbols (e.g. T's, 9's). A note about the usage of 's found on the NOAD says:
There are a few special instances in which it is acceptable to use an apostrophe to indicate plurals, as with letters and symbols where s added without punctuation could look odd or be undecipherable (dot your i's and cross your t's; he rated a string of 9.9's from the jury). However, when forming plurals of regular nouns it is wrong to use an apostrophe, e.g. six pens not six pen's.
A note about the usage of the apostrophe says the following:
Many people are uncertain when to use an apostrophe, and this confusion is probably increased by the fact that it is often omitted in company names (e.g. Barclays Bank). The apostrophe should be used when indicating possession (Sue's cat) or the omission of letters or numbers (he's gone, 1 Jan. '09). It should not be used in forming the plural of ordinary words, as in apple's and pear's or I saw two dog's, or in possessive pronouns such as hers, yours, or theirs.