Increasing your sites speed is an increasingly important factor for Google the leading search engine, if your site is not responsive enough, then two negatitive consequences can be seen.
Firstly the page crawl depth in your site will be reduced, which is a big problem if you have a large site with millions of pages such as our Reporting Accounts one
Secondly pages get pushed down in the Search Engine Results Placement if their speed is not as good as the sites in their niche.
A site I use a lot for this purpose is one called webpagetest
What is great about this site is that it shows you the issues, suggests recommendations and by much following those would improve things, plus you can do a side by side comparison with your competitors.