Are all Muslims supposed to follow Prophet Muhammad's example?
Building on Mohammad Sakib Arifin's answer, I'd like to emphasize how many times following the Prophet Muhammad is mentioned in the Qur'an:
Say (O Muhammad SAW to mankind): "If you (really) love Allah then follow me (i.e. accept Islamic Monotheism, follow the Quran and the Sunnah), Allah will love you and forgive you of your sins. And Allah is Oft-Forgiving, Most Merciful." -- Qur'an 3:31
These are the limits [set by] Allah, and whoever obeys Allah and His Messenger will be admitted by Him to gardens [in Paradise] under which rivers flow, abiding eternally therein; and that is the great attainment. -- Qur'an 4:13
And whoever obeys Allah and the Messenger - those will be with the ones upon whom Allah has bestowed favor of the prophets, the steadfast affirmers of truth, the martyrs and the righteous. And excellent are those as companions. -- Qur'an 4:69
He who obeys the Messenger has obeyed Allah; but those who turn away - We have not sent you over them as a guardian. -- Qur'an 4:80
O Prophet, sufficient for you is Allah and for whoever follows you of the believers. -- Qur'an 8:46
And whoever obeys Allah and His Messenger and fears Allah and is conscious of Him - it is those who are the attainers. -- Qur'an 24:52
There has certainly been for you in the Messenger of Allah an excellent pattern for anyone whose hope is in Allah and the Last Day and [who] remembers Allah often. -- Qur'an 33:21
It is not for a believing man or a believing woman, when Allah and His Messenger have decided a matter, that they should [thereafter] have any choice about their affair. And whoever disobeys Allah and His Messenger has certainly strayed into clear error. -- Qur'an 33:36
He will [then] amend for you your deeds and forgive you your sins. And whoever obeys Allah and His Messenger has certainly attained a great attainment. -- Qur'an 33:71
There is not upon the blind any guilt or upon the lame any guilt or upon the ill any guilt [for remaining behind]. And whoever obeys Allah and His Messenger - He will admit him to gardens beneath which rivers flow; but whoever turns away - He will punish him with a painful punishment. -- Qur'an 48:17
And what Allah restored to His Messenger from the people of the towns - it is for Allah and for the Messenger and for [his] near relatives and orphans and the [stranded] traveler - so that it will not be a perpetual distribution among the rich from among you. And whatever the Messenger has given you - take; and what he has forbidden you - refrain from. And fear Allah; indeed, Allah is severe in penalty. -- Qur'an 59:7
Yes. Allah says in the Quran (interpretation of the meaning):
Certainly you have in the Messenger of Allah an excellent exemplar for him who hopes in Allah and the latter day and remembers Allah much.
Yes all Muslims are supposed to follow prophet Muhammad (Saw), because Allah has sent him to us as an example to follow for any believing man and woman, failure to follow him one will face the wrought of Allah... " Oh Allah make us follow the footstep of prophet muhammad."