When developing a new website, it is imperative to remember that the user should always be in control of their browsing experience and that they are viewing your website primarily for your content (which in turn will affect their decision to interact with you further). Having said that, there are a few frequent "annoyances" found on websites which can impair this experience:
Disabling browser functionality
Autoplaying video content
Video content has become commonplace thanks to services like Youtube and Vimeo and can add an extra level of interactivity to any website. While it is tempting to make these videos autoplay in order to get the user's attention (and increase your view count), autoplaying videos are considered highly annoying and can easily disrupt the user, especially if they are listening to music beforehand. Autoplaying videos can also be very disruptive to screen reader users. Most video hosting services will offer the option to disable autoplay when embedding.
Modal overlays (aka lightboxes)
These are pop-ups that appear frequently on websites asking you to take a survey, subscribe via e-mail, like product x on facebook/twitter and so on. While this isn't an annoyance in itself, in most cases the pop-up will obscure the content (usually by dimming the rest of the browser window so the pop-up is in focus) until you either close the pop-up or interact with it. These can be really irritating to your intended audience as it blocks out your content until the user interacts with it; your content should always be the main attraction of your website and is more important than gaining that extra like on facebook or another follower on twitter.