I'm quite interested in specific aspects of history such as this, especially how people well-known today were perceived in their times. Considering Shakespeare's works are still quite widely performed today, I was wondering how much fame Shakespeare had in his time.
Here's an excerpt from an answer I gave to a similar question a week or so ago:
Lying on his deathbed in 1592, playwright Robert Greene wrote an insulting passage about an overrated 28-year-old poet:
...there is an upstart crow, beautified with our feathers, that with his tiger's heart wrapped in a player's hide supposes he is as well able to bombast out a blank verse as the best of you, and being an absolute Johannes factotum is in his own conceit the only Shake-scene in a country.
That is the earliest known mention of William Shakespeare as a playwright. In 1592 he would have been a playwright for less than 3 years with 4-7 plays under his belt and he was already popular enough to deserve the derision of Greene, England's first celebrity author.
After 1594 it is safe to presume that Shakespeare was among the most well-known playwrights in the London theatre scene because he had become the in-house playwright for the Lord Chamberlain's Men of which he owned a 12.5% share. The LCM was a big deal as acting troops went. They already had England's most sought-after actor. By 1599 they had England's best theatre. By 1603 they had become King James I's (and therefore England's) official acting company. By 1607, chances were pretty good that if you knew the name of only one London playwright, that name was either William Shakespeare or Ben Johnson.
One piece of evidence for Shakespeare's success in his own time is the publication and sale of his plays (often without his permission) with his name on the cover. John Shakespeare (Will's father) was granted a coat of arms (probably financed by his son's success) in 1596. In 1597, at age 33, Shakespeare was able to purchase New Place, one of the largest houses in his home town, while still living and working in London. Shakespeare's will is the best indicator of his prosperity, revealing a desire to set up a family dynasty by leaving the lion's share of his wealth to his first child, Susanna.
I'll be happy to answer any followup questions you might have.
