Is there a specific number of times that one should visit Makkah?

Whoever makes any claim about Islamic teachings
should produce sound evidence. Allaah says (interpretation of the meaning):

“… Say: ‘Produce your proof
if you are truthful.’ ” [al-Baqarah 2:111]

So it is not permitted to accept anyone’s
opinion without evidence or proof. What evidence is there that a Muslim should
visit Makkah seven times and Bayt al-Maqdis (Jerusalem) once in his lifetime?!

Allaah has made it a duty to perform Hajj once
in a lifetime. The Prophet (peace and blessings
of Allaah be upon him) said: “O people, Allaah has made Hajj a duty upon
you, so perform Hajj.” A man asked, “(Should we do it) every year,
O Messenger of Allaah?” but he remained silent. The man asked the question
three times, then the Prophet (peace and blessings
of Allaah be upon him) said: “If I say yes, it will be obligatory for you,
and you will not be able to do it.” Then he said: “Do not push me
to tell you more than I have told you. Those who came before you were destroyed
because they asked too many questions and argued with their Prophets. If I command
you to do something, then do as much of it as you can, and if I forbid you to
do something, then leave it well alone.” (Reported by Muslim,
2380)

Allaah says (interpretation of the meaning): “And
perform properly (i.e., all the ceremonies according to the ways of Prophet
Muhammad), the Hajj and ‘Umrah (i.e., the Pilgrimage to Makkah) for Allaah…”
[al-Baqarah 2:196]

The person who performs Hajj and ‘Umrah
once in his lifetime does not have to do them again, but it is encouraged to
repeat Hajj and ‘Umrah, because the Prophet
(peace and blessings of Allaah be upon him) said: “Follow up one Hajj or
‘Umrah with another, for they eliminate poverty and sins as the fire eliminates
dross from iron, gold and silver. An accepted Hajj brings no less a reward than
Paradise.” (Reported and classed as hasan by al-Tirmidhi, al-Sunan,
738). The Muslim who is capable and healthy is encouraged not
to stay away from the Ancient House (i.e., the Ka’bah) for too long, as
Abu Hurayrah reported that the Messenger of Allaah
(peace and blessings of Allaah be upon him) said: “Allaah says: ‘If
a slave to whom I have given good health and ample provision does not come to
visit Me once every five years, he is indeed deprived.’” (Reported
by Ibn Hibbaan and others; see Saheeh al-Jaami’, 1909).

All of the above reports indicate that frequent visits to Makkah
are encouraged, but they are not obligatory.

As far as visiting Bayt al-Maqdis (Jerusalem)
is concerned, if a Muslim never visits it in his lifetime, there is nothing
wrong with that. There are no obligatory acts of worship connected with it,
but it is the third of the great Mosques which a Muslim is permitted to travel
to visit; it is not permitted to travel to any other place for the purpose of
prayer and worship, except these three mosques. The Prophet
(peace and blessings of Allaah be upon him) said: “No one should set out
on a journey (of pilgrimage) except to three mosques: Masjid al-Haram [in Makkah],
the Mosque of the Messenger of Allaah (peace and
blessings of Allaah be upon him) and Masjid al-Aqsaa [in Jerusalem].” (Reported
by al-Bukhaari, 1115). The reward for praying in Masjid al-Aqsaa
will be multiplied over the reward for praying in any other mosque, apart from
Masjid al-Haram in Makkah and Masjid al-Nabi (peace
and blessings of Allaah be upon him) (The Prophet’s Mosque) in Madeenah.
The author of Mughni al-Muhtaaj said: “It has been proven that prayer
in Masjid al-Aqsaa is worth five-hundred times more than other prayers, as was
reported by Ibn ‘Abd al-Barr; al-Bazzaar said: its isnaad is hasan.”

Jaabir ibn ‘Abd-Allaah said: “The Messenger of Allaah
(peace and blessings of Allaah be upon him) said:
‘One prayer in this Mosque of mine is better than a thousand prayers in
any other mosque except for al-Masjid al-Haram, and one prayer in al-Masjid
al-Haram is better than one hundred thousand prayers offered elsewhere.’”
(Reported by Imaam Ahmad; see also Saheeh al-Jaami’, 3838).

And Allaah knows best.