One of the well known Unix/Linux commands is tail, which gets the tail of a file, meaning the end of a file and prints it out to the output stream.
I used to try find nice programs for this, including Baretail which has some very nice features like colouring lines in that match certain patterns etc.
But if you just want a simple, and now built into Windows solution, just use PowerShell:
Get-Content -Tail 10 filename.txt
This will show the last 10 lines of the file. You can even follow the tail, or watch it for changes, as below:
gc -Tail 10 -Wait filename.txt
Another nice thing you can do is then pipe this into Select-String to filter the output:
gc -Tail 10 -Wait filename.txt | Select-String -Pattern somepattern