My problem definitely started after the 10.10.3 upgrade.
I've never used Chrome before, but I just installed that. No issues at all. Side by side, I can browse the same sites with Chrome and Safari, with Chrome always getting to the site quickly. Safari is always slower, but occasionally just freezing- and needing further action like described above to continue to make progress.
To my knowledge, no other networked application is having problems except the Safari browser (App Store is also occasionally slow, but I don't think related). For me, it is about 1/5 pages will freeze. The blue bar will start to move across the URL bar. Then just stop. Sometimes it continues to move slowly. I usually intervene by putting the cursor in the URL bar and hitting enter to reload the page. Usually that helps, not always.
Again, no issues with Chrome. Guess my answer is to stop using Safari until I see that there is some fix.