To my comment, 
<I think the main difference is that not getting married is bitul
of a mitzvah.  Not going on the Har Habayis when one has no korban to
bring is not.>,

RYMedad responded:
<Besides the matter that korbanot were not the only reason to be 
on/in the Har Habayit, if I am not mistaken, the Rambam and others 
include building the Bet Hamikdash as a mitzvah and in doing so, we 
can afford for the Jewish people the opportubnity in one form or 
another to fulfill some 200+ mitzvot.>

      While his statement is true, it is also irrelevant to the 
discussion, since those currently visiting the Har Habayit are not 
engaged in the building of the Beis Hamikdash. 

RnSBoublil responded to my remarks:
<I was reading the material presented in Sidur HaMikdash, Shabbat 
regarding Mitzvot to be performed in the Mikdash itself, and 
apparently Korbanot are not the only mitzva.

<A. There is a Mitzva min HaTorah to enter Har HaBayit for prayer and 
Ze'aka when a Ta'anit is called, when Am Yisrael is in danger (Sefer 
HaMitzvot Rambam, Aseh 59 and Hilchot Ta'aniyot 1:a), for example: 
during water; plague; lack of rain; or other Pur'Anuyot.  It is a 
Mitzva both during the time of the Bayit and when it's BeChurbano.

<At this time, they are supposed to blow on Chatzotzrot HaKesef and a 
shofar (described in Mishna Rosh Hashana 25;a and Rambam).

<Shaliach Tzibbur adds 7 special blessing to the prayers with a 
special ending and during which Cohanim Tok'im UMeri'im (see Rambam 
there, chapter 4 and especially halachot 16-17). 

<This gathering is held Davka near Sha'ar HaMitzrach of Har HaBayit 
(NOT the Kotel) so that as many as possible can partake, including 
Tmei'ei Meit and Tevulei Yom.>

     Neither in the Sefer Hamitzvos nor in the Yad does the Rambam 
indicate that the mitzvah involves the Har Habayis.  When it _is_ 
done there, certain aspects of the mitzva change, but it is no more 
mitzva there than elsewhere.   In any event, since the Sha'ar 
haMizrach is not a place on the mountain but specifically the 
entrance to the Azarah, it presupposes the existence of the Bayis.

<B. There is a special mitzva to do Teki'ot Rosh HaShana Davka on Har 
HaBayit (mishna Rosh HaShana 3, 3 and also 27;1).>

     Again, there is no indication that there is a special mitzva to 
blow on the Har.  There is a special way of doing the general mitzva, 
but no obligation on anyone to do it there.  Furthermore, here too 
the Mikdash is required, not just the Har. (Rambam Hilchos Shofar 
1:2 -- "BaMikdash hayu tok'in.")

<C. There is a special mitzva of Netilat Lulav on Sukkot during all 7 
days davka on Har HaBayit (see Sefer HaMitzvot Rambam mitzva 169). It 
was not cancelled b/c of the Churban.>

     Here, too, it is the Mikdash, at least according to the Rambam, 
who writes (Hilchos Lulav 7:13) "uvaMikdash l'vado not'lin oso b'chol 
yom vayom mishivas y'mei hechag."

<These 3 are just examples. There are many others examples and 
special tefillot which are answered davka if said on the Har HaBayit 
itself.>

     As noted, none of the three are examples.  I doubt that there 
are any which apply in the absence of a Mikdash.  I am also unaware 
of the special t'filos referred to, and would appreciate examples.  
In any event, as above, those who are going on the Har today are 
engaged neither in the special ta'aniyos, nor shofar blowing, nor 
fulfilling mitzvas lulav.  They are chancing issur kareis, while 
fulfilling no mitzva.

EMT