Seriously belated edit: If you're using .NET 4.0 or later
The File class has a new ReadLines method which lazily enumerates lines rather than greedily reading them all into an array like ReadAllLines. So now you can have both efficiency and conciseness with:
var lineCount = File.ReadLines(@"C:\file.txt").Count();
Original Answer
If you're not too bothered about efficiency, you can simply write:
var lineCount = File.ReadAllLines(@"C:\file.txt").Length;
For a more efficient method you could do:
var lineCount = 0;
using (var reader = File.OpenText(@"C:\file.txt"))
{
while (reader.ReadLine() != null)
{
lineCount++;
}
}
Edit: In response to questions about efficiency
The reason I said the second was more efficient was regarding memory usage, not necessarily speed. The first one loads the entire contents of the file into an array which means it must allocate at least as much memory as the size of the file. The second merely loops one line at a time so it never has to allocate more than one line's worth of memory at a time. This isn't that important for small files, but for larger files it could be an issue (if you try and find the number of lines in a 4GB file on a 32-bit system, for example, where there simply isn't enough user-mode address space to allocate an array this large).
In terms of speed I wouldn't expect there to be a lot in it. It's possible that ReadAllLines has some internal optimisations, but on the other hand it may have to allocate a massive chunk of memory. I'd guess that ReadAllLines might be faster for small files, but significantly slower for large files; though the only way to tell would be to measure it with a Stopwatch or code profiler.