You may not be able to run your own email or instant messaging server software but you may know a trusted entity (friend, organization) who (knows someone who) runs his own server and can create an account for you: a server you can trust and which does not do business by collecting your data. On your side, you need some appropriate software that additionally does crypto, and there we go!
A quick example:
an open standard for instant messaging is XMPP (formerly called Jabber);
existing XMPP servers I trust are jabber.ccc.de and xmpp.telecomix.org (it is also possible to run one yourself);
easy-to-use FLOSS clients allow you to connect to any XMPP server: Pidgin (with the OTR plugin for encryption) for Windows and GNU/Linux, Adium for Mac OS, Jitsi for these three platforms, Gibberbot for Android, etc.
See? No need of a US-based Gmail, Facebook or a Russia-based ICQ. Go further with other usages, by consulting this or this lists of relevant software.
This article does deliberately not cover in detail software solutions and technical considerations, nor issues related to the need of anonymity and to the importance of meta-data. It shows that decent privacy improvements can be made with little effort and that it can make a substantial change if massively applied. You can move on with this good pedagogical introduction from Quinn Norton.
So, remember: decentralization and cryptography through appropriate tools and behavior.
Do not expect laws to efficiently protect your privacy, as secret services will increasingly have means to silently and massively circumvent law obligations.
If governments wanted to promote privacy (and, through this, free speech and democracy), they would setup teaching of these key concepts to children at school and would promote FLOSS and internet decentralization. For now, they are mostly going the opposite way - corruption talks.