I'm not sure if there's a "Delphi 2010" way, but there is a Windows way that doesn't involve FindFirst and all that jazz.
I threw together this Delphi conversion of that routine (and in the process modified it to handle > 4GB size files, should you need that).
function FileSize(const aFilename: String): Int64;
var
info: TWin32FileAttributeData;
begin
result := -1;
if NOT GetFileAttributesEx(PWideChar(aFileName), GetFileExInfoStandard, @info) then
EXIT;
result := info.nFileSizeLow or (info.nFileSizeHigh shl 32);
end;
You could actually just use GetFileSize() but this requires a file HANDLE, not just a file name, and similar to the GetCompressedFileSize() suggestion, this requires two variables to call. Both GetFileSize() and GetCompressedFileSize() overload their return value, so testing for success and ensuring a valid result is just that little bit more awkward.
GetFileSize*Ex*() avoids the nitty gritty of handling > 4GB file sizes and detecting valid results, but also requires a file HANDLE, rather than a name, and (as of Delphi 2009 at least, I haven't checked 2010) isn't declared for you in the VCL anywhere, you would have to provide your own import declaration.