There are a few alternatives (like the Atlassian products that Dexterity pointed out, or have a look at this list from alternativeto.net) - but I've found Slack to be mega useful for small teams. We still use some Atlassian products (like JIRA, Bitbucket and Confluence) in conjunction with Slack - but Slack's not designed to replace the Atlassian products.
So the major benefit of Slack, for us, is that it's free and puts everything into one place. There's a fee if you want infinite integrations and to store your message history forever, whereas the free version limits these. You can also split your workstreams into separate #channels, which we have ~20 of to keep tasks separate between PM's, BA's, Design, Dev, and QA.
It already integrates with Dropbox and Google Drive, and has its own functionality for private messages. For now, you'd still have to use Skype and Gmail separately - though Slack's recently bought out Screenhero, so that'll negate the need for Skype as well soon. Though just out of interest, why are you using Dropbox and Google Drive? For collaboration purposes, I'm assuming?
Anyway, I guess this is more personal experience rather than an answer... but you can't really go wrong with Slack. It's removed the need for constant emails, and has really improved communication for us.
Maybe check out the Slack Tour quickly and sign-up if it sounds like it'd fit your requirements? I don't work for Slack but can't recommend it enough. Plus, with it being free, you've got nothing to lose by trying it out at least.
Hope this helps!