At the moment I have spybot installed and certainly avast 4.8.
Is it still necessary to have a separate spyware-tool or are tools in avast enough? Is there a better free spyware tool than spybot?
It is not enough. Better have SAS and ST (SuperAntiSpyware (free) & Spyware Terminator (free)). BOCLEAN is also good on Comodo site. Search this forum as this subject has been discussed in lenght! 
Short answer is NO!
there are real-time load at boot time protection
and
there is “on demand” keep on your hard drive to use as needed which take no resources unless used
you need Avast as an AV
you also need one of the real-time anti malware- anti spyware
either Spybot T-timer
or
Spyware Terminator free WITHOUT THE AV or add on bho toolbar!
or
Windows Defender
or- several other choices
But ONlY have ONE “installed” loads at boot time (plus AVAST)
you can have as many “on demand scanners” as your hard drive can hold
keep Spybot with or without t-timer turned on
update and re-immunize every Wednasday
what version spybot- if you have EVER had 1.3 or 1.4 post back!
lots of folks like MBAM as an on demand scanner with one of the above real time protection
lots of opinions here
SAS is a good one
see also this current thread
http://forum.avast.com/index.php?topic=38152.0