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Given a set of random data points on a map, I would like to cluster the data points based on number of data points in a cluster, time to travel within all the data points in the cluster,and/or number of clusters needed. Is there a way or extension in ArcGIS Desktop that can automatically create the cluster?

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Without more details in your Question, it is difficult to be certain of your precise requirements. However, I think your best starting point may to review the help page entitled An overview of the Mapping Clusters toolset:

The Mapping Clusters tools perform cluster analysis to identify the locations of statistically significant hot spots, cold spots, spatial outliers, and similar features.

You may also want to review How to find Clusters of N Points Within X Distance?

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