Invoke-Sqlcmd -query "select getdate(), getdate()+1" -serverinstance "yourservername"|Export-Csv c:\temp\testps2.txt –notypeinformation
or, broken down by line so you can see all of it...
Invoke-Sqlcmd 
 -query "select getdate(), getdate()+1" 
 -serverinstance "yourservername"
 |Export-Csv 
 c:\test\test.txt 
 –notypeinformation
-query: the query.
-serverinstance: server name
-notypeinformation: removes the “#TYPE System.Data.DataRow” line at the top.
And if you don't want a header row... you have to use a different export process, and then tell a different process to iterate through the array and write to disk.  Really, guys?  Too hard to add a -noheader option?
(and all this is on one line; you can use a ` to split it across lines.
Invoke-Sqlcmd -query "select getdate(), getdate(); select getdate()+1, getdate()+1" -serverinstance "yourservername"|ConvertTo-Csv -notypeinformation -outvariable outdata; $outdata[1..($outdata.count-1)] |ForEach-Object {Add-Content -value $_ -path "c:\temp\test.txt"}
or 
Invoke-Sqlcmd -query "select getdate(), getdate(); select getdate()+1, getdate()+1" `
-serverinstance "ftw-sv-db-03"|ConvertTo-Csv -notypeinformation -outvariable outdata;`
 $outdata[1..($outdata.count-1)] |ForEach-Object {Add-Content -value $_ -path "c:\temp\test.txt"}
 (then hit enter again to tell it you're done for realsies)
Oh, and it for some reason outputs the full file to console, but saves what you want to a file.