Since opening my own agency I've received, on average, about 60 queries by post and another 40 queries by e-mail each week. That's 100 total queries a week, or 443 or so queries a month, or about 5,215 queries a year. I've asked some agent friends about this, and these numbers are roughly comparable to what they receive, though a few colleagues at the big agencies get more.
My first priority is to my present clients, and this is what takes up the biggest chunk of my time. On any given day I might be reading a client's new mystery, editing a non-fiction proposal, submitting a debut novel to publishers, conducting an auction, pitching the book to foreign publishers, negotiating an option, chasing down a payment, etc.
My next priority is to read works that were referred to me by clients, agents, or editors. In truth, this is the pool where many of my new clients come from, and it's also necessary to attend to these materials to ensure that your relationships with the referrer remains positive.
If there's a free chunk of time during the week I'll try to tackle the unsolicited queries. Reading queries can be mundane work, so I'll often avoid looking at them until I'm in the correct mindset. I have an assistant that helps sort everything (for example, poetry, romance, science fiction in the far future or set on a different planet, and erotica are almost always immediate rejections), but I do like to give each query a read-through.
If you want to improve your chances, here are some simple things you can do that will avoid agents' ire and insure that your query gets the attention it deserves.
Use standard A4 envelopes or bigger for your SASE (self-adhesive preferred but not essential). Spell the agent and agency's name right (its Jonathan, not Jonathon). Don't shorten an agent's name to present a sense of familiarity (I have never gone by Jon or John, and I know plenty of Richards who don't like to be called Dick, and Christinas who don't want to be called Christ unless they're freaks). Any of the above is just sloppy; authors wanted to work with diligent agents, and the reverse is true as well.
Next, please, please don't tell me that you want to sell your copyright. You are licensing rights to publishers, not selling your copyright (unless it's a work-for-hire). I'm anal-retentive (as my dear friends tell me all the time), but these are your legal rights we're talking about here! You should know what you're getting involved in.
Please, please don't tell me that you think this is an Oprah book. I want all my clients to go on Oprah, and some might be a good fit for her show, but the chances are slimmer than a supermodel that this is going to happen. Also, don't tell me I'll be making the biggest mistake in the world if I don't take you on. Confidence is essential in this business (for both authors and agents), but cockiness isn't.
Read the agent's submission requirements. Some agents like a query and synopsis, some like a query and sample chapters, and some want a whole proposal. Almost all want a SASE. Some only want e-mail queries, some never want e-mail queries, some want you to use their website to submit, and some won't respond to your e-mail query unless the project interests them (like me).
Finally, be patient. Try to remember how many queries an agent gets each week. We can rush through them and get back to you within a few days without properly considering your work, or you can give us time and we can evaluate your query with the proper care.