I have depression, and because of this, my attendance at college and
my grades have been compromised.  It is very likely that after this
semester I will be academically dismissed for good from the
university.  I do however, have an associate's degree in arts from a
community college (Kishwaukee Community College and I am attending
Northern Illinois University).  Will other colleges accept you after
you have been academically dismissed from one school?  This includes
colleges from the same state, colleges in other states and colleges in
other countries.  Will they accept your credits as transfer (as with
the associate's degree) or will you need to start from scratch?

Directly from the NIU handbook 

Reinstatement 
A student dismissed for academic deficiency may seek reinstatement by
written petition to the dean and the Academic Standing Committee. The
committee will recommend to the dean that petitions for reinstatement
be granted only if it finds: (1) that there is a likelihood that the
student will be able to raise his or her cumulative GPA to 2.000 by
the end of the academic year of reinstatement and to maintain this
standard for the remainder of his or her academic career, and (2) that
there were material events or circumstances of an unusual nature,
beyond the student's control, that significantly affected his or
ability to perform; or, for students who have completed only one year,
that there has been a significant improvement in academic performance
during the second semester. The final determination will be made by
the dean. No student may be reinstated more than once.

as far as other Universities go , it depends on their specific rules
but a rule of thumb is

skip one semester , apply for reinstatment , if reinstated you are on
probation for the semester and have to keep up your GPA , if you pass
the semester you are reinstated for good

I know of a similar case to yours here in the UK where a 2nd Year
Student was actually dismissed.

Fortunately, there was a Complaints Mechanism and she was reinstated
after she truthfully reported that she had been suffering from
depression.

She backed up her request for reinstatement with a note from her doctor.

Good Luck!

I echo pronopublico's comment and would add that dismissing you
because you have been unable to complete the course satisfactorily
through illness could be regarded as contrary to disability
discrimination legislation.

Even if you are dismissed (or resign) *on health grounds* it should
not stop you being accepted at a university in future - again this
could be contrary to disability discrimination legislation.

At any future applications you should make an effort to be frank about
this period of time whilst making it clear that it was a temporary
problem which has now been resolved and will not hinder your future
prospects.

All the best

Owain

I am dealing with very similar situation right now.  Ive been
suffering from severe depression for about 2 years and last semester
it really impacted my performance (i actually failed my first class
ever).  This was my first semester in college and i was put on
probation with a 1.15 qpa. This semester i worked as hard as i could
through the depression because i knew i needed to raise my qpa.  I
received two B's, a C+ and a C this semester but bc of the credit
difference in the classes it apparently wasnt enough to get out of
probation and im now being dismissed.  I just want you to know i
understand the helpless feeling you get from knowing you are capable
of achieving a certain level of performance and having something as
powerful as depression holding you back.  I dont have any advice for
you on (re)applying to colleges bc im trying to figure that out right
now too but i hope you get through everything.  If you get a chance,
let me know what you end up doing (applyinhg to another
school...applying for reinstatement?)
good luck
-Ashley