Islam has (at least) two separate promised figures: the Mahdi, "the guided one, and the Masih, the Messiah, who in Islam is Jesus but not the Son of God. Neither have any more to do with Muhammad than Jesus had to do with Moses, that is to say, they're seen as separate figures in the same sacred tradition. Together they will fight the Al-Masih ad-Dajjal, Anti-Christ, at the end of times.

Several people have claimed to be one or the other of those figures. Here are a few important ones.

The Bab in 19th century Iran claimed to be the Mahdi, and promised one great than him. Most Babists became Baha'is, when Bahaullah claimed to be the Mesih (and much more--he claimed to be the promised one of essentially all religions). This is the basis of the modern Baha'i Faith, which probably has about six to eight million adherents worldwide. It also has some of the most beautiful sacred architecture in the world.

Mirza Ghulam Ahmad apparently claimed to be both the Mahdi and the Masih in 19th century South Asia. His teachings are the basis for the modern Ahmadiyya faith, which may or may not be separate from Islam. There are two main Ahmadi groups. The larger is called Ahmadiyya Muslim Community (sometimes the last word is left untranslated as Jamaat), the smaller called the Lahore Ahmadiyya Movement. Both believe he was the Mahdi and Masih, but the Ahmadiyya Muslim Community claims he was a prophet, while the Lahore Ahmadiyya Movement explicitly denies that possibility (they claim when Ahmad himself spoke of being a prophet or a messenger, he was speaking metaphorically). Ahmadis are harder to estimate than Baha'is as they are more likely to be in Muslim majority countries and to some degree hidden. There's probably fewer than a million Lahoris (maybe fewer than 100,000) and maybe in excess of ten million mainstream Ahmadis.

There's apparently another surviving Mahdi-inspired group, the Mahdavia, in South Asia today, following a 15th century Mahdi claimant, but I know little about them.

And of course Twelver Shi'a believe that the 12th Imam was the Mahdi, who is not dead, but become "occulted" in the 9th century. Oh and the Nation of Islam teaches that Wallace Fard, who disappeared in Detroit in the 1930's, was the Mahdi and Masih.

There have been movements that didn't survive and eventually disappeared/merged back into mainstream Islam. The most important was Shah Ismail, who conquered Azerbaijan and Iran in the 16th century and founded the Safavid dynasty. He claimed to be the Mahdi (and the reincarnation of Ali for good measure). He used this messianic fervor to fuel his campaigns, but after military defeat he suffered a real crisis of faith. None of the later members of his dynasty treat him as the Mahdi and instead, they bring in Lebanese Shi'a clergy to Iran (which had been, up to that point, Sunni).

In the 19th century, there was the infamous "Mahdist War" in Sudan against British rule that was also defeated militarily (though they were initially one of the most succussful instances of indigenous military to British rule). In the 20th century, the 1979 Seige of the Grand Mosque in Mecca was also initiated by a Mahdi claimant, and there are no followers of this movement as it too was defeated military.

There have been many, many more. Wikipedia has a list.

I would actually make a rare point of disagreement with /u/yodatsracist in that to my reading there is a history of such claims of the reincarnation of Muhammad in some of the Ghuluw (i.e. the "exaggerator") traditions of Shiite heresies. Other branches, while being less explicit, to my reading in their gnostic and esoteric beliefs imply the return of the Prophet Muhammad, or are at least purported to believe as such by the heresiographers who are our primary sources for the historical beliefs of such groups.

So you have the "Mimiyya" or the "Muhammadiyya" who believed:

In their system (as described by Sa d b. Abd Allah al-Kumml) Muhammad is both the unknown God,and God's only true manifestation on earth. God first appeared before mankind as a light, calling upon them to acknowledge his oneness. They refused, and this was apparently the act of rebellion that initiated the fall from heaven. God then appeared in human form so that his creatures might trust him and not fear him. He appeared (but only to the Arabs, it would seem) as successive prophets and messengers: Adam, Noah, Abraham, Moses and Jesus; to the non- Arabs he appeared as successive kings and rulers of the world. Mankind still refused to confess his unity, and so he appeared in the form of a number of Imams, and was then accepted. Of these Imams, only members of the ahl al-kisa [q. v.] are mentioned by name. They are (in addition to Muhammad) Ali, Fatima(God can assume the form of a woman), al-Hasan and al-Husayn, who together constitute the divine pentad. The Imams are reincarnations of God; as such they are mere illusions or "names" concealing the true "meaning" (maana) which is Muhammad. A parallel structure incorporates other elect members of the community, all of whom are arranged in a hierarchical fashion. Thus God's only true messenger or "gate" (bab) is Salman al-Farisi [<7-fl.], who appears with Muhammad before Arabs and non-Arabs; other abwab, who include various leaders of the Kufan ghulat, are reincarnations of Salman. The normal obligations of Islam (prayer, fasting, etc.) were imposed as a punishment on those who deny the truth, and are not incumbent upon believers who have passed the test (mu'min mumtahan). The spirits of those who deny the truth transmigrate through both animate and inanimate bodies (tanasukh), and end up as minerals or stones. The believer who acknowledges the truth, in contrast, passes through seven stages, each lasting 10,000 years, during which he wears seven different bodies like seven garments (akmisa): when he outgrows one garment, he puts on another. After 70,000 years he becomes a gnostic (arif) and attains knowledge of the ultimate (ma'rifat al-ghaya): the veil is removed and he sees God, that is Muhammad, in his essence and light.

All of these groups of the "exagerators" of the divinity of Muhammad or of Ali are no longer extant, except for the Alawites, historically known as the Nusayris, who have nonetheless, to my understanding, significantly moderated their views and are basically quite close to orthodox Twelverism. Their belief in metempsychosis implies to me at least the reincarnation of Muhammad:

You can see what I mean about their doctrines from their entry in the Encyclopaedia of Islam below:

As ghulat, the Nusayriyya venerate Ali b. Abi Talib as supreme and eternal God (al-ildh al-azam, al-kadim al-azal). The basis of Nusayri doctrine is a cosmogony of gnostic nature (Sulayman, Bdkura, 59-61; Halm, Gnosis, 298 ff.). In the beginning of time, the souls of the Nusayris were lights, surrounding and praising God; then they rebelled against Him, disputing His divinity. From then onwards, they have been hurled down from the celestial heights and exiled on the earth, where they are enclosed in material bodies and condemned to metempsychosis (temporal nasukhiyya for the elect, eternal nasukhiyya for the damned). During their fall, the supreme God appears to them seven times, calling for their obedience, but they refuse. In each manifestation, God,who is called "the Essence" (maana), is accompanied by two subordinate hypostases, "the Name" (ism) which is also called "the Veil" (hidjab) and the "Gate" (bab). In earthly life, this trio is revealed in numerous instances: the maana is incarnated successively in Abel, Seth, Joseph, Joshua, Asaf, St. Peter and Ali b. Ali Talib, then in the imams as far as the eleventh one, al-Hasan al- Askari; all of these are therefore manifestations of divinity. However, their true character is veiled by the presence of the hidjab or ism (Adam, Noah, Jacob, Moses, Solomon, Jesus and Muhammad), each of them is accompanied by a bab. The central trio of the Islamic period is Ali (maana), Muhammad (ism, hidjab) and Salman al-Farisi (bab). The abwab of the eleven imams are the intermediaries between the concealed divinity and initiated believers; for example, the eponym of the Nusayriyya, Muhammad b. Nusayr, was the bab of the eleventh imam al-Hasan al- Askari, whose secret revelations he confided exclusively to the Nusayriyya.

I'm not enough of a specialist in these heresies to know where the scholarship stands on this but to my reading at least these suggest the reincarnation of Muhammad.

Source wise, both quotations are from the respective entries on "Muhammadiyya" and "Nusayriyya" in the *Encyclopaedia of Islam", the entry on "Ghuluw" is also worthwhile.

edit: accidentally left in a bit before I checked the wider entry on Ghuluw, finding the entry on Muhammadiyya.

Nope.

Muhammad himself is considered to be the reappearance of a divine principle called the "mim" or "ism." The "mim" is the first entity to be emanated from the divine being Itself (the "ayn" or the "mana"). While Muhammad was alive, Muhammad's cousin (Ali), was considered to have been a representation of the "ayn." Likewise, the legendary figure, Salman the Persian, was considered to have been a representation of the "bab" or the "Holy Spirit" (AKA Gabriel).

The moment Muhammad received his first revelation was a time when all three persons of the trinity were present: Allah (Ali), the Messenger (Muhammad), and Gabriel (the go-between between Ali and Muhammad).

Nusayris (some) believe that Jesus was an "incarnation" of the "ayn." The moment Jesus was conceived (Jesus, being God (Allah)), He was veiled by Mary (the ism/hijab), and placed into the veil/womb by the Holy Spirit (i.e. "conceived through the Holy Spirit"), AKA the "bab." (The bab functions as a go-between between the first two persons of the trinity. So in Jesus' conception, God was placed in the womb of God (the veil or ism) by the bab (the "Holy Spirit"). Similarly, during Muhammad revelation, God (Ali) gave revelation to Muhammad (the ism), through Gabriel (the Holy Spirit, or the bab).) (In the Sunni tradition, Gabriel (Jibril) is often called the Ruh al-Qudus, or the "Holy Spirit.")

This is the origin of the Islamic tradition that Jesus was the only infant never to have been touched by Satan upon His birth. (This is a Sunnite tradition by the way.)

So whenever the trinity reveals Itself, all three members are always present.

The "mim" (and the "ayn" and the "sin") are recurring figures in history who always reappear. Muhammad is the "last Prophet," however, not because he is the last appearance of the mim, but because religion in general will remain in its current form until the End of Time (the Day of Judgment, often called: the Hour). This is specifically why Muhammad claimed to be the completion of the Prophetic building in the famous "brick metaphor." After Muhammad's coming, religion had assumed its complete and final form. Hence the Quranic verse: today I have completed My favor unto you and chosen for you Islam as your religion. (The words of Allah, apparently.)

Muhammad claimed that after his death, the caliphate would disappear after 30 years. This prediction came true after the death of Ali. Ali, combined with Abu Bakr, Umar, and Uthman, total 30 years of "Rashidun" khalifa. Muhammad also claimed that his community would be ruled by twelve amirs. The first of these amirs was Ali, the last was Hasan al-Askari.

The final amir would also bring back khalifa near the End of Time, he is generally identified with the Mahdi (a genetic descendant of Muhammad who would restore khalifa, rule the world, and eliminate injustice and poverty in general). So, for most of Muslim history, the Ummah was ruled by unsuitable individuals.

There is a Madhavia sect that maintains a site called Khalifatullah Mehdi, one of the texts on that site maintains that the Mahdi is on the same level as the Prophet (in terms of stature). This is just a roundabout way of saying that the Mahdi and the Prophet are both the "mim." A Nusayri explanatory book by Yaron Friedman quotes al-Tabarani (famous Nusayri theologian) as saying that the all the laws are one (all shariah or divine commandments are the same) since it is the mim in all appearances (so in this sense, Moses, Adam, Muhammad, the Buddha and so on were all the same person). Since only the mim can erect or a establish a religion upon divine guidance, in some sense, the Mahdi and Muhammad "are" the same person. This is ultimately why the Sunni tradition maintains that the Mahdi and the Prophet will have "the same name" and that their "fathers' names would be the same."

The appearance of Isa, or Jesus, at the End of Time, assisting the Mahdi, is probably the reappearance of the ayn, since the ayn is usually "externally" subordinated to the mim. Although the truth is that the ayn is God, whilst the mim is a servant.

Hope that makes sense.

tl;dr

The historical person, Muhammad, will never come back. But, a coming back of his person, in-essence, will return as the Mahdi, to re-establish Islam the universal religion, restore the caliphate, and bring about world peace (accomplish Islam all over the world).