The danger of taking it all a bit too seriously...
The Covering Letter. If you're an author with an agent (or, more crucially, an author trying to get an agent), then you'll know exactly what this is. Put simply, in your head, it's The Most Important Letter You Will Ever Write.
Realistically, we all know success or failure of a submission rests upon the quality of the manuscript, on your ability to actually grab and hold the reader's attention. But we also know agents are busy people with targets to hit and money to earn. If a bad covering letter provides the excuse they need to elbow your masterpiece off a crowded desk into a bin already overflowing with the hopes and dreams of countless other aspiring writers, the pressure is on to ensure you don't make those sharply-tailored limbs twitch with longing to reject from the moment the submitted pages flutter into their in-tray.
In my long and boring secretarial career, I wrote thousands of letters, and was always sufficiently meticulous to guarantee neat presentation, clarity of message, correct spelling...but I didn't care about a single one of them. I knocked 'em out, read 'em through, pp'd 'em, bunged 'em in an envelope, slapped on a stamp, and got on with the rest of my life. Bish, bash, bosh - five minutes from start to finish, and that included swearing at the uncooperative office printer, whacking it repeatedly with a high-heeled shoe until it spat out the document you were waiting for, and turning the place upside-down looking for a respectable envelope. By very stark contrast, every covering letter I've ever written has taken a number of weeks, several drafts, some background research, and lashings of needless anxiety.
Telling a writer not to worry is like telling a dog not to pant, but it seems barmy to be so irrationally uptight about something as straightforward as writing a letter, especially when I doubtless would have churned it out in the usual milliseconds without hesitation if asked to compose one for somebody else, and probably made no less competent a job of it.
Please remember that, as long as it isn't riddled with howlingly-obvious spelling errors, isn't a glaring display of spectacularly agent-riling arrogance, and definitely isn't drenched with assertions from your mother as to your literary brilliance (of course she thinks you're fantastic, she made you! What she's really doing is patting herself on the back!), then it's pretty likely most agents will at least turn from the letter to the first page of your manuscript, which is where you want them to be anyway. In that sense, as an introductory tool, your letter, however 'imperfect', has done its job. Well done. The months agonising over those four tiny paragraphs were worth it. There's still a hefty chance the agent will read the opening half-page of your manuscript, roll her eyes, extend that shoving elbow and file the whole lot under 'B', but you cleared the first hurdle, and that's the role of the covering letter. Unfortunately, the next fence is much higher...
There's a wonderful Charles Schulz 'Snoopy' cartoon that I have pinned above my desk. It's the covering letter I'm not quite brave enough to write. It shows Snoopy at his typewriter, and reads thus:
'Gentlemen, enclosed is the manuscript of my new novel. I know you are going to like it. In the meantime, please send me some money so I can live it up.'
Nuff said?