What is the size limit for Logcat and how to change its capacity?

As already mentioned, you can see the size of the circular buffer with logcat -g. On my Galaxy Nexus, it's 256 KB:

shell@android:/ $ logcat -g
/dev/log/main: ring buffer is 256Kb (255Kb consumed), max entry is 4096b, max payload is 4076b
/dev/log/system: ring buffer is 256Kb (0Kb consumed), max entry is 4096b, max payload is 4076b

If you need to save a continuous log longer than that, you can just open a new adb shell and type

logcat -f myfile.log

This command redirects log entries to the file myfile.log on an ongoing basis, and won't return until you hit ctrl-c to stop it. Now go back to your original adb shell and type the command you wanted to log, and all its output (more than 256 KB in my case) will get saved to myfile.log.

Since Android 5.0, Developer Options shows/allows increasing the size of ring buffer.

To see the size use -g

$ adb logcat -g
ring buffer is 64Kb (63Kb consumed), max entry is 4096b, max payload is 4076b