If you are using google webmaster then you may probably seen few 404 page not found errors for your blog.If this error is persist for few days then you should fix this problem otherwise it may affect your blog page rank.
I faced this problem in my blog.I solved this 404 error page problem using following techniques.
404 Error Pages will come due to few reasons like if your migrating your blog from blogger to wordpress and changed the permalink then after few days your blog posts will have new permalinks structure and old one will show 404 error.
If you are using google webmaster tool then you can download the 404 error pages from crawl errors pages link.
Add 404 error pages one by one in above location.Within few days this 404 error pages will remove from google search results.
If you are using wordpress platform then download Broken Link Checker plugin then activate that plugin it will detect all the broken link from your blog.Go to 404 error pages and unlink those pages.
You can also create 404 custom pages (like above)for your blog then redirect your visitors to your blog home page.It will also increase your blog traffic.
Let me know if you have few more options for 404 error pages problem.