I left my previous job two years ago and started my own business (in
California) in the same industry as my previous employer (supplying
corporate housing). My previous employer had me sign a contract
stating that I will not pursue any of their customers to try and get
their business. Because there is no time limit stated in the contract,
does that mean I may never seek out any of their customers for ever
and ever or is there a reasonable time limit to this type of contract.
And, how enforceable is a contract of this type.

The general rule regarding clauses of this type is that they must be
reasonable in temporal and geographic scope.  California law may be
different, but I doubt it.  So, for example, such a non-compete
clause, as they are called, might try to preclude competitive conduct
by a former employee for one year in the county in which the former
employer is located.  That clause would likely be held enforceable
since those are reasonable temporal (one year) and geographic (the
county) limitations.  Conversely, if such a clause stated that the
former employee could not compete for eternity in the whole
world--well, you see my point.

If your clause has no duration, is there a geographic limitation
stated?  Does it just say any customers wherever located?

The rationale behind the limitations on such clauses is that it is
unconscionable to prevent a man from earning a livelihood for too long
in too broad an area.

Note that even if your clause is found to be unenforceable as being
overly broad in temporal or geographic scope, that does not mean that
you can violate trade secrets laws by sharing your former employers
trade secrets with the customers if in fact you do contact them.

Does your former employer consider his customer list to be a trade
secret?  If so, that would preclude you from actually taking a copy of
the list with you when you left, but that does not preclude you from
using residual memory of the clients and contacting them based solely
on your residual memory of the list and not the physical, actual list
itself.

Need to clarify:  if your employer considers his customer list a trade
secret and if it IS a trade secret under relevant state law, then you
could not take a copy of the list OR

I am having a hard time today.

Need to clarify:  if your employer considers his customer list a trade
secret and if it IS a trade secret under relevant state law, then you
could not take a copy of the list OR use the list contents, even if
you did not have a noncompete clause.  But that does not mean that if
you contact one or two former customers (assuming such conduct does
not otherwise violate the noncompete clause) who you know to be
customers due to your residual memory of the list, that that would be
a trade secrets violation.

California law *is* very different from many other states as far
non-compete agreements are concerned.  California law is among the
least favorable toward non-compete agreements, although there are
situations under which non-compete agreements are enforceable, even in
California.  Your agreement does not seem reasonable in duration,
since no duration is specified.  The trade secret issue is another
issue.

But, it really doesn't matter what advice you get here.  You really
need to talk to a lawyer who is licensed in California.  Before a
legal problem occurs is when you should talk to a lawyer, not after
the problem has already occurred and everyone is mad.  If you want to
deal with some of the same clients as your former employer, spend a
little money now on legal consultation, and get genuine legal advice. 
A little money now, and you can greatly reduce the odds of needing to
spend the cost of a house fighting a 10 year lawsuit that ends up
accomplishing very little for you or the other side.

Thanks to all who commented! Excellent feedback. I'm going to cancel
the request for an answer because I feel I have enough to make my
decision. By the way, there wass no confidential list of
clients/customers, my former employer did business with
anyone/everyone so it seems only fair I should be able to do the same.
Thanks again.

ANother point:  I don't know if your former employer has a continuing
relationship with his customers or if the latter get served and the
relationship is then ended.
Obviously  - says the layman! -  the contract you signed could only
apply for customers that were such at the time you left.  If that
employer now has a new customer, and you also happen to approach that
customer, it would not seem that this could be a breach of the
contract.

BUT -  ...  only a lawyer can tell you for sure.