Here's how to do it with a one-dimensional problem.
In[1]:= res =
Reap[NDSolve[{y'[t] == y[t], y[0] == 1}, y, {t, 0, 1},
EvaluationMonitor :> Sow[y[t]]]];
In[2]:= res
Out[2]= {{{y -> InterpolatingFunction[{{0., 1.}}, <>]}}, {{1.,
1.00009, 1.00009, 1.00018, 1.00018, 1.00471, 1.00471, 1.00926,
1.00926, 1.01383, 1.01383, 1.03331, 1.03331, 1.02801, 1.02801,
1.0424, 1.0424, 1.05699, 1.05699, 1.07178, 1.07178, 1.10199,
1.10199, 1.13305, 1.13305, 1.16498, 1.16498, 1.19781, 1.19781,
1.23157, 1.23157, 1.31583, 1.31583, 1.40584, 1.40584, 1.50202,
1.50202, 1.60477, 1.60477, 1.71456, 1.71456, 1.83185, 1.83185,
2.02451, 2.02451, 2.23743, 2.23743, 2.46616, 2.46616, 2.71828,
2.71828}}}