No!
If tables were not to be used at all for your code, they would have been taken out. Tables have a proper use, and that use is for tabular data! This is the time to use them (not for presentation or design). So by all means, use tables!
I would recommend to provide a caption tag within your tables to give people who may be using screen readers (such as blind Web surfers) proper context, too.
Example:
<table>
<caption>Corporate Information of Current Employees</caption>
<tr>
<td class="employeeName">Jim Jones</td>
...
Don't be afraid of current trends. Tables should be used for tabular data. You're doing it right :)
Dive Into Accessibility offers a lot of helpful tips, as well.