Is there an easy way, and/or, is there a conversion program ??
Are you wanting to store all of these data in a geodatabase? Do you have a certain file type container that you want to use? How many shapefiles do you have?
If you just want shapefiles and not some other format... you are done!
The shapefile format is independent of the ArcMap version AND it can be used in many other software packages.
To expand on what Adrian Welsh is suggesting, if you decide you want to convert all the shapefiles to feature classes in a File or Personal Geodatabase, and you have many of them, there are a couple of ways to automate that process:
Also, if you are not sure if you want to consider using shapefiles or not, here's some info that may help in making a decision:
Geoprocessing considerations for shapefile output
Chris Donohue, GISP
To build on to what Chris Donohue, GISP was saying (utilizing a batch process to convert your shapefiles into geodatabase), there are some resources online you could utilize (or build a model through ModelBuilder and/or utilize a Python script to do this).
Here is a very old 'resource' I found from Esri's site to do this (assuming it still works):
Convert shapefiles and coverages to a geodatabase in batch mode
Or, here is a blog post that describes a simple way:
Migrating your existing data into the Geodatabase | ArcGIS Blog
Retrieving data ...