As it happens, I work in the time and attendance industry.
Your alternatives depend on what your needs are. For instance: whether you're tracking time just for yourself or for employees, how many employees you have, what type of business you have, what your budget is, and why you're tracking time.
For instance, if you're tracking time for the purpose of preparing payroll for your employees, there are all sorts of software-based solutions. You have your choice of software installed on your computer or hosted on the service provider's computer. You can pick input options ranging from punching in at your computer to terminals (keypad, badge or biometric) to telephony. Most of these will export employee hours worked to your payroll software or service bureau to save payroll prep time and eliminate clerical errors.
Especially if you're outside the United States, or if you're in one of the states like California that have their own quirky wage and hour rules, you'll want to make sure the software you're contemplating can accommodate your local regulations.
Costs can range from a one-time purchase of less than $100 to thousands of dollars, depending on the sophistication of the software and the number of employees you need to track.
If for some reason software doesn't work for you, you can always rely on the old faithful punch clock. There are newer electronic models that will automatically total employees' hours, so they offer some of the time-saving and accuracy-enhancing benefits of software. But you still have to key the time in to your payroll software or service bureau, so the potential for keying errors is still there.
For software, the 900-pound gorilla in the market is Kronos. But their packages might be overkill for most entrepreneurial and micro sized businesses. There are a zillion others, many of which specialize in web-based products: Tsheets, Time America, TimeTECH, TimeTrex, TimeForce, etc. Just do a search on "time and attendance software" to find a whole pile of companies.
There are several companies that offer both software and traditional punch clocks: Acroprint Time Recorder, Amano Cincinnati, Icon Time, Lathem Time, Pyramid Technologies, etc. You can buy their products directly from most of these, as well as from networks of local dealers and from retailers such as Staples, Office Max and Office Depot.
If you're tracking time for salaried exempt professionals for the purpose of billing clients for the time they've spent, there are also numerous software solutions. One I'm personally familiar with is the time tracking feature in Freshbooks. It isn't intended to track work time for payroll purposes, but it will do a good job of tracking time spend on different projects for billing purposes. It's particularly well-suited for solo practitioners and small teams.
Bottom line: there are all sorts of alternatives
to ordinary time sheets.