This is a very lucrative class of programs and consequently the very best programs are unfortunately, commercial products. However, with the increase of 'open source' programming there are viable alternatives available without paying a penny.
I have been researching a few new products which aren't yet listed below. I hope to update you all soon and until then here are a few suggestions.
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The best of the free programs is "Timesheets Lite" from Moving Target Software. It's actually an older "lite" version of that company's full featured $32 shareware product. Its main limitation is that only one person can be connected to the program's database at any one time.
That aside, Timesheets Lite has all the features needed for anyone who bills on a time or project basis. Reporting is not possible without having Excel installed on your computer but this shouldn't be an issue for the majority of users. It can also export timesheet data to Excel for easy invoicing.
If you are looking for a completely free web based solution try Live Time Online. It offers Time Sheet recording, reporting and invoicing with no restrictions on the number of projects or users. It is compatible with most browsers and there is no need to install any software which is a bonus. Invoicing is built in so theres no need to have Excel installed as with other options.
If you want an alternative consider Timesheet Xpress Free. The free version is limited to a single account but if you can live with this it's worth checking out. The vendor's web site offers a "Cinderella" version - the full product becomes the free version after 35 days. A feature comparison is also available on the website.
You might want to check out these articles too:
Live Time Online
Timesheet Xpress Free