Thumbs up for Ukraine (EDIT: and Kazakhstan, apparently) which do not require a visa from EU citizens! Europeans can stay for up to 90 days and can do what they like, apart from working.
However Russia and Belarus require letters of invitations (referred to as "LOI") and the visas are very restrictive. There are several horror stories floating around about people messing up and getting literally thrown out of Russia... The policies seem to vary depending on location of embassy and the nationality of applicant, even differing between policies for different EU countries.
For my big trip to Russia in 2011, I would like to have a very generous Russian visa for the longest possible period, with multiple entries. I don't want to be tied to staying with one particular location/hotel/organisation, at least not for more than a night or two.
Does anyone know a competent and reliable organisation or individual who offers a service for this, i.e. fills in all the paperwork in a way that will satisfy the the visa bureacrats...?To get the kind of visa I want I think I will have to stretch the truth a tiny bit...