Please answer as many of the following questions as you can. You may already have answered some of them. In that case, there's no need to repeat the answers.
Have you restarted your router and your broadband device (if they're separate) since you first noticed the problem? If not, do that now and see whether there's any change.
If your browser is Safari, then from the Safari menu bar, select
Safari ▹ Preferences... ▹ Privacy ▹ Remove All Website Data
and confirm. Any change?
If you're running OS X 10.9 or later, select the Advanced tab in the Preferences window and uncheck the box marked
Stop plug-ins to save power
Any change?
Quit and relaunch the browser. Any change?
Log out and log back in. Any change?
Enable Private Browsing in the Safari menu. Any change?
Are any other web browsers installed, and are they the same? What about other Internet applications, such as iTunes and the App Store?
If other browsers and Internet applications are also affected, follow these instructions and test. Any change?
If Parental Controls is active for any user, please turn it off and test. Any change?
If only Safari is affected, launch the Activity Monitor application and enter "web" (without the quotes) in the search box. If a process named "Safari Web Content" is shown in red or is using more than about 5% of a CPU, select it and force it to quit by clicking the X or Quit Process button in the toolbar of the window. There may be more than one such process. Any improvement?
Open the iCloud preference pane and uncheck the box marked Photo Stream, if it's checked. Any change?
If you can test Safari on another network, is it the same there?
If you connect to your router with Wi-Fi and you can also connect with Ethernet, do that and turn off Wi-Fi. Any difference?