I have a cyanogenmod phone without google for 6 months : I use F-droid as a market. The main advantage is that you can add other repository. Thus I have the classical F-droid one plus the guardianproject one but you may add others one.
For my "evryday wihout google" life I use : *K-9 mail (+APG) for my mails (Apache2) *Gibberbot for XMPP conversation (it deals OTR and can even be used in google talks ) (Apache2) *Firefox as webbrowser (MPL2) *duckduck go apps as search engine (Apache2) *The Diaspora webclient (GPLv3) *Jamendo to listen music (Apache2) *KeePassDroid to manage my password (GPLv2) *Offline Calendar as a calendar without synchro (he is efficient but ugly :/) (MIT) *OsmAnd as maps and GPS stuff (GPLv3) *Yaaic as an irc Client (GPLv3+) I don't have problems when browsing except on youtube.... :P Hope this may have help you.