Word Processing Software
Most computers come loaded with a word processing application like Word Pad or Star Office or Microsoft Word. Any of these can be used to put together a line by line list of your collection and plug new items in manually as you acquire them. This is the least expensive option, but it's also the most limited because sorting will need to be done manually.
General Database Software
Programs like Open Office or Microsoft Excel can be your baseball card database. Of course, setting up a database can be tricky, so you will need to have some prior knowledge to get started. It is also more limited than a program designed specifically for baseball card collections.
Beckett
Beckett, which produces price guides for sports cards, has a free service that allows you to enter your collection in its database. This option can be appealing because users can easily access and sort information. You can also show off your collection to other collectors, make trades and easily get updated values.
ETopps
If your collection is made up entirely of Topps baseball cards, you can use the free online system provided by that card manufacturer at etopps.com. It has automatic updates to alert you when cards you list as wanted go on sale. It also helps you put cards on sale through eBay listings tied directly to your account.
Shareware
In general, shareware is software that can be downloaded and installed for free. There is usually some limitation (perhaps number of entries or a time limit) and you have to pay and unlock the program for full functionality. There are quite a few shareware baseball card collecting programs including the Baseball Card Collector Professional, which allows charting; the Sports Card Collector that also has a catalog for non-baseball sports cards; and C2PRO, which helps create reports that can be easily exported.