I'm considering dropping off / posting leaflets to local small businesses to advertise my web & graphic design services.
Is this kind of promotion acceptable or might it just result in people getting annoyed?
Like any advertising venture, leaflets or fliers can be beneficial.
If you think the local market would produce some clients this way, then by all means I'd try it. Costs are really minimal compared to possible returns. You wouldn't need anything overly fancy, a simple well designed, clear, one-color flier, which is merely copied rather than printed, would suffice.
I think it depends heavily on a few things:
I'm not saying don't do it, but you need to consider some of the extra work required.
What about posting on bulletin boards around town? What about your local Chamber of Commerce (or similar)?
To be candid, I think you'd be better of spending your money on a few pints than chopping down trees and throwing them to the wind. :) I've been traveling around the world doing web and software development for about two decades now. Dropping of pamphlets is as effective as direct mail marketing (it's not). Since you are in the web & design business, you would be much better served by attending networking events (meetup.com events, Toast Masters, conferences, InterNations, etc). Studies show that the response rate to direct mail marketing is around 4%. Much less still are actually converted into a sale. From my own experience, you're better served chatting it up at building a great portfolio online, chatting it up at networking events, and handing out a card like there is no tomorrow. See if you can get a chance to get up and speak at these events and be sure to plug your company as much as possible. Many of these events won't let you self-advertise, so arrive dressed as a human billboard.