  We study the holographic and agegraphic dark energy models without
interaction using the latest observational Hubble parameter data (OHD), the
Union2.1 compilation of type Ia supernovae (SNIa), and the energy conditions.
Scenarios of dark energy are distinguished by the cut-off of cosmic age,
conformal time, and event horizon. The best-fit value of matter density for the
three scenarios almost steadily located at $\Omega_{m0}=0.26$ by the joint
constraint. For the agegraphic models, they can be recovered to the standard
cosmological model when the constant $c$ which presents the fraction of dark
energy approaches to infinity. Absence of upper limit of $c$ by the joint
constraint demonstrates the recovery possibility. Using the fitted result, we
also reconstruct the current equation of state of dark energy at different
scenarios, respectively. Employing the model criteria
$\chi^2_{\textrm{min}}/dof$, we find that conformal time model is the worst,
but they can not be distinguished clearly. Comparing with the observational
constraints, we find that SEC is fulfilled at redshift $0.2 \lesssim z \lesssim
0.3$ with $1\sigma$ confidence level. We also find that NEC gives a meaningful
constraint for the event horizon cut-off model, especially compared with OHD
only. We note that the energy condition maybe could play an important role in
the interacting models because of different degeneracy between $\Omega_m$ and
constant $c$.
