I was reading Minhat Yehuda. In the book, the Tzadik Rabbi Yehuda Fatiya asks the destroying angels what they are like.
The angels mentioned things like how they ate manna, had kids, died, etc.
So my question is, in the world to come or Gan Eden is there intercourse?
I ask because intercourse can be a holy act.
The Talmud (Berachot 17a) states:
העולם הבא אין בו לא אכילה ולא שתיה ולא פריה ורביה ולא משא ומתן ולא קנאה ולא שנאה ולא תחרות אלא צדיקים יושבין ועטרותיהם בראשיהם ונהנים מזיו השכינה שנאמר ויחזו את האלהים ויאכלו וישתו
In the future world there is no eating nor drinking nor propagation nor business nor jealousy nor hatred nor competition, but the righteous sit with their crowns on their heads feasting on the brightness of the divine presence, as it says, And they beheld God, and did eat and drink.
(Soncino translation)
While the term פריה ורביה does not necessarily include all sexual activity, Maimonides when codifying this (Hilchot Teshuvah 8:2) is more explicit:
כך אמרו חכמים הראשונים העולם הבא אין בו לא אכילה ולא שתיה ולא תשמיש אלא צדיקים יושבים ועטרותיהם בראשיהן ונהנין מזיו השכינה
Thus, the Sages of the previous ages declared: "In the world to come, there is neither eating, drinking, nor sexual relations. Rather, the righteous will sit with their crowns on their heads and delight in the radiance of the Divine Presence."
(Touger translation)
To clarify Alex's answer, the term "world-to-come" is ill-defined in Judaism, and for different authors, and different writings it means different eschatological stages. We can basically divide it into three distinctive realms:
Usually, to have sex (as we know it, unless it's Bullock and Stallone in "Demolition Man") you need a functioning body. So automatically, option #1 is irrelevant.
Regarding option #2 Rambam explicitly suggests that sex would be practiced during that era:
"Our Sages have said that there is no difference between This World and the Days of the Messiah except (our) subservience to the kingdoms of the world alone." Mishneh_Torah Kings_and_Wars.12.2
Now regarding option #3, here Rambam somewhat hits the wall when he discusses the "world-to-come" in Hilchot Kings and Wars (ibid), and unlike his recap on the aforementioned Gemmora in Hilchot Teshuva, he states that not only that the future is impossible to know, but we have no tradition:
"But regarding all these matters and similar, no one knows how it will be until it will be. For these matters were unclear to the Prophets. Even the Sages themselves did not have a Tradition regarding these matters and only could attempt to understand the verses. Thus, there were disagreements in these matters."
So how do we resolve Rambam's discrepancy? My personal approach to reconciling two Rambams without refuting either statement is to declare some of his statements as "educational" and not "factual". Because he saw himself as an educator, many of his statements (Sefer Hamadah especially) focus on "experiential truth" rather than "factual truth". Just like we don't care to be precise when we instruct our kids ("if you touch those wires you'll die"), or like God, when he said: "for as soon as you eat of it, you shall die.”
Therefore, Alex's popular answer is not factual (as it refutes Rambam in Kings), but rather educational, meaning that undoubtedly, in some final idealistic form, there will only be the highest form of purely spiritual enjoyment, but the exact details are sealed.
However, there's another option, that the sages (Berachot 17a and Rambam in Hil. Teshuva) did not refer to #2 and #3 on my list, but called afterlife "the world-to-come". And we're back to square one - to my opening sentence.
NB: You asked about some mysticism. According to the Kabbalistic tradition, this world is the Tikkun to the primordial sin (i.g. Adam and Eve having some kind of improper sex on Friday, instead of waiting for Shabbos and doing it the right, spiritual way). So after the world is fixed, we're supposed to move into Eden, namely having the status of "Adam and Eve before the sin".
But apparently, they were intended to have sex on Shabbos. Therefore, if the world-to-come is called "the day that will be completely Shabbat and rest in everlasting life., and we're back to Eden, we are going to have sex. The proper way, of course. No idea what could be. A happy ending!
