HDD Guardian is a free open source tool which uses SMART (Self-Monitoring, Analysis and Reporting Technology) to check and display the health of compatible hard drives.
Launch the program and its Overview tab displays a basic system summary: your hard drives (SMART doesn't apply to USB keys or other devices), their temperature, reliability score, bad sectors, ATA errors and more.
The Manage tab expands on this, in particular with a "S.M.A.R.T. attributes" section which lists all the drive's raw data (spin up time, power on hours, head flying hours, it's all here).
The Manage tab also gives access to more advanced settings and options. You're able to set a spindown timer, adjust the drive Advanced Power Management setting, enable/ disable write caching and read look-ahead, run various SMART tests, even turn SMART off entirely if you can think of a reason to do so (note, most of these options need administrative rights).
Typically you'll probably just run HDD Guardian to query drives on demand, but the program can also manage and display error logs for each device. If you're particularly concerned, it's also possible to run the program in the background, and be alerted to any problems via an icon in your system tray. And an extensive Settings dialog even includes an option to receive email alerts (see Settings > Mail alerts).
Note that this is the portable version of HDD Guardian.