It has previously been shown that readers spend a great deal of time skim reading on the Web and that this type of reading can affect comprehension of text. Across two experiments, we examine how hyperlinks influence perceived importance of sentences and how perceived importance in turn affects reading behaviour. In Experiment 1, participants rated the importance of sentences across passages of Wikipedia text. In Experiment 2, a different set of participants read these passages while their eye movements were tracked, with the task being either reading for comprehension or skim reading. Reading times of sentences were analysed in relation to the type of task and the importance ratings from Experiment 1. Results from Experiment 1 show readers rated sentences without hyperlinks as being of less importance than sentences that did feature hyperlinks, and this effect is larger when sentences are lower on the page. It was also found that short sentences with more links were rated as more important, but only when they were presented at the top of the page. Long sentences with more links were rated as more important regardless of their position on the page. In Experiment 2, higher importance scores resulted in longer sentence reading times, measured as fixation durations. When skim reading, however, importance ratings had a lesser impact on online reading behaviour than when reading for comprehension. We suggest readers are less able to establish the importance of a sentence when skim reading, even though importance could have been assessed by information that would be fairly easy to extract (i.e. presence of hyperlinks, length of sentences, and position on the screen).