Any way to check the clock speed of my processor?

From the command line type lscpu. The information will be at CPU MHz:

~$ lscpu | grep MHz
CPU MHz:               804.901
CPU max MHz:           3200.0000
CPU min MHz:           800.0000

There are a couple of ways:

1. lscpu or more precise lscpu | grep "MHz".
   This will give you the general MHz for the CPU.

    $ lscpu | grep "MHz".
    CPU MHz:               1600.000
   

2. cat /proc/cpuinfo or more precise cat /proc/cpuinfo | grep "MHz".
   This will give you the individual MHz for each CPU Core. So if you have an Core 2 Duo, AMD Bulldozer, Core i7, etc.. it will show the MHz for each core.

   $ cat /proc/cpuinfo | grep "MHz"
   cpu MHz     : 1600.000
   cpu MHz     : 1600.000
   cpu MHz     : 1600.000
   cpu MHz     : 1600.000
   cpu MHz     : 1600.000
   cpu MHz     : 1600.000
   cpu MHz     : 1600.000
   cpu MHz     : 3400.000
   

3. lshw -c cpu or more precise version: lshw -c cpu | grep capacity
   Will give you the general MHz. Same as lscpu.

   $ lshw -c cpu | grep capacity
   WARNING: you should run this program as super-user.
          capacity: 1600MHz
   WARNING: output may be incomplete or inaccurate, you should run this program as super-user.
   

4. sudo dmidecode -t processor or more precise: sudo dmidecode -t processor | grep "Speed" Will not only give you a MHz in use but also the Maximum you can push / overclock your CPU to.

    $ sudo dmidecode -t processor | grep Speed
    [sudo] password for cyrex: 
        Max Speed: 4000 MHz
        Current Speed: 2666 MHz
   

Out of all of this, lshw and dmidecode provide the best information out of your CPU.

You can also target the current MHz detected by the kernel by querying the log files:

cat /var/log/dmesg | grep "MHz processor" - For the current detected MHz speed

cat /var/log/kern.log | grep "MHz processor" - For the current and past detected MHz speeds. Will not work in some cases, that is why I posted the dmesg one first.

And that's all I can remember from the top of my head. I am fairly certain there are other ways, just don't remember right now. Of course, talking about terminal ways.

Note: All the commands above will also give you the CURRENT cpu Hertz, meaning, if you expect to see the same one on lscpu and when doing the cat /proc/cpuinfo it will be near impossible. you CAN compare the maximum because that should show the same for any of the ways you can analyze the CPU, but the current will always be literally "the current CPU hertz" at the moment you execute it. Lastly do note that dmidecode reads information from the ACPI tables which is not always the same as the real time ones done by the other tools.

For the current CPU speed one can dynamically watch this change in real time using:

sudo watch -n 1  cat /sys/devices/system/cpu/cpu*/cpufreq/cpuinfo_cur_freq

To see the maximum CPU speed, use:

cat /sys/devices/system/cpu/cpu*/cpufreq/scaling_max_freq 

indicator-cpufreq-selector is a nice little indicator tool which shows your current cpu frequency. You can even select the desired cpu frequency.

However last update for this tool was on 2015-10-19.

This works fine for real-time processor speeds

 watch "grep 'cpu MHz' /proc/cpuinfo"

While this is active, you can also spam the processor to see what maximum real-time speeds it can reach by openssl speed

I'd like to point out sudo is needed for Ian's answer above:

sudo cat /sys/devices/system/cpu/cpu*/cpufreq/cpuinfo_cur_freq

However you can get the same results without sudo using:

cat /sys/devices/system/cpu/cpu*/cpufreq/scaling_cur_freq

My favourite is to use Conky where you can paint your own picture:

This sits on the right of my built-in display all the time. The relevant code for the CPU section is:

${color2}${voffset 5}Intel® i-7 3630QM 3.4 GHz: ${color1}@  ${color green}${freq} MHz   
${color}${goto 13}CPU 1 ${goto 81}${color green}${cpu cpu1}% ${goto 131}${color3}${cpubar cpu1 18}
${color}${goto 13}CPU 2 ${goto 81}${color green}${cpu cpu2}% ${goto 131}${color3}${cpubar cpu2 18}
${color}${goto 13}CPU 3 ${goto 81}${color green}${cpu cpu3}% ${goto 131}${color3}${cpubar cpu3 18}
${color}${goto 13}CPU 4 ${goto 81}${color green}${cpu cpu4}% ${goto 131}${color3}${cpubar cpu4 18}
${color}${goto 13}CPU 5 ${goto 81}${color green}${cpu cpu5}% ${goto 131}${color3}${cpubar cpu5 18}
${color}${goto 13}CPU 6 ${goto 81}${color green}${cpu cpu6}% ${goto 131}${color3}${cpubar cpu6 18}
${color}${goto 13}CPU 7 ${goto 81}${color green}${cpu cpu7}% ${goto 131}${color3}${cpubar cpu7 18}
${color}${goto 13}CPU 8 ${goto 81}${color green}${cpu cpu8}% ${goto 131}${color3}${cpubar cpu8 18}
${color1}All CPU ${color green}${cpu}% ${goto 131}${color1}Temp: ${color green}${hwmon 2 temp 1}°C ${goto 250}${color1}Up: ${color green}$uptime

I would just like to add i7z to this list. Contrary to the other options, this works better for CPUs in the i7, i5 and i3 series that have TurboBoost.

This is my favorite:

watch -n1 "grep 'MHz' /proc/cpuinfo"

Although if you have Turbo Boost (or Turbo Core if AMD), you may prefer the following, which uses cpupower from the linux-tools group:
_{* On my system, both work equally well though.}

sudo watch -n 1 -d cpupower monitor

Thanks @Zanna for point out the useless use of cat in the comments.

If you are using an embedded ARM device (such as a Raspberry or ARM based phones), you will not be able to use solutions using lscpu, dmidecode or /proc/cpuinfo because the current speed is not listed there, if the tool is at all available. Instead you have to use sysfs:

alias getcpuf='i=1; for x in $(sudo cat /sys/devices/system/cpu/cpu*/cpufreq/cpuinfo_cur_freq); do y=$(($x/1000)); echo "CPU-${i}: $y MHz"; i=$((i+1)); done;'

# getcpuf
CPU-1: 600 MHz
CPU-2: 600 MHz
CPU-3: 600 MHz
CPU-4: 600 MHz

sudo powertop then hit Tab twice to get to the "Frequency stats" tab.

It displays Actual frequency (accurate on my Laptop, as opposed to dmidecode), along with stats about how long is spent in each available frequency.