I like to keep mine online, rather than local...that way its accessible from whichever device I'm using at the time.
For online programs (and probably US specific, since that's where I am)...
Ancestry is actually free, and they provide access to limited records databases. For a subscription fee, you can access even more records data as well as other people's trees. Its very easy to use, and you can control the privacy levels of your tree. I leave mine public, but use it mostly for my playground and research tree, so I may have mistakes and errors in my tree.
FamilySearch is also free, and has free access to most of the same records that Ancestry has. But its a "one world tree", rather than your own individual tree. So its more difficult to use it as a research playground, and difficult to control the accuracy of what others introduce.
WikiTree is also free, and is a lot like FamilySearch, in that it too is a "one world tree", but without the records databases. Its easier here to collaborate with others and manage the accuracy, but perhaps more difficult to use as a research playground, since profiles can't really be deleted. One of the best things about WikiTree is the wiki-style biographies, because stories and history about our ancestors are so much more interesting than just plain facts and data.
I tried MyHeritage once, but didn't need yet another tree. Didn't really care for it.
I'm sure there are others, but I think these are the big ones.
Locally, there are also a number of Open Source programs available. I've had a couple recommended to me in the past, but I've forgotten them now -- since I tend to prefer keeping my trees online anyway.