Depends what you mean by 'productivity apps', that's a broad market :) There's also more than a little personal preference involved. Here's some random suggestions that I've found useful:
Todoist is something I've found useful. I've tried a few similar services, and keep coming back to it.
Used to be an Evernote user, but the last nail in the coffin was crippling the free tier by limiting to two devices. I'm trying OneNote out as a replacement, seems to be an improvement so far.
Teamwork Projects has been useful, and I prefer it to the other project management tools I've used.
I've used Wrike on and off. I like its low-friction nature, though for some reason it doesn't really 'stick' for me. It might for you.
I find Insightly CRM to be a useful tool. There are many CRM services out there, but only a small number with a free tier that isn't completely hobbled. Agile CRM and Hubspot CRM are others, each with their own take on things. I like Insightly's 'linking' methodology, though.
Both Asana and Podio are 'swiss army knives' that are useful when you need something structured but a little different from the mainstream.