There are plain-vanilla verbs, and there are Rocky Road-with-chocolate-sauce-and-whipped-cream-verbs. The verbs you choose will make a difference in your fiction.
Sentences that use walked, sat, and thought pale in comparison to stalked, sprawled, and stewed. However, don't label yourself as a failure if strong verbs don't automatically show up in your manuscript. Adding stronger verbs is something you do in your rewriting.
The purpose of your first draft is to get the story on the page, in all it's unedited glory. Once you've got it down, you can analyze it for overuse of adverbs, adjectives, cliches--and wimpy verbs.
Here are a few resources to help you tackle the job.
Dragon Writing Prompts has compiled a massive list of 1000 strong verbs to take the place of weak ones. The list is grouped by verb: for example, she has dozens of strong verbs to use in place of "walked" or "ran". I'm planning to print out the list and keep it handy. And Coherent Visual has a similar, downloadable list in both Word and .pdf formats.
Charlotte Rains Dixon posted a two-part post on strong verbs. The first is What is a strong verb?, and the second continues with How to ferret out strong verbs.
Creative Juices Books lists seven reasons why strong verbs are important (and when to use passive verbs).
Carolyn Jewel shares why strong verbs help you write with strength and specificity, and why "to be" should be your verb of last resort.
Bob and Jack's writing blog gives a number of great examples of both strong and weak verbs.
Give it a try right now. Take a random page of your manuscript and highlight every verb on the page. Count how many are "plain vanilla" and substitute some stronger verbs. When you read it again, how much better is it?