This app was mentioned in 8 comments, with an average of 7.00 upvotes
I suggest money manager EX... I tried almost every app around and I just keep comming to it, it's opensource and no ads, also has windows, mac, linux clients.
Link: Money Manager Ex for Android
edit: added link manually, bot linked other app.
A bit late, I used to use Monefy, then Money Manager Ex, but I'm using Wallet now as the UI is cleaner.
I use Wallet because it supports having different currencies, scheduled transfers and payments (unlinked to anything, purely for budgeting purposes), and there are no ads. You can also set goals and handle debts with it. The main reason I use it is because of the UI really. It's clean and simple. I can display as much or as little as I want. You have to have a premium account if you want to export your data though.
Money Manager Ex is more detailed if you have a lot going on with your finances. I think it allows data export for free too.
Money Manager Ex is where my search ended. Excellent free software without any limitation. Data can be easily synced between desktop and mobile version.
What's this about an online only solution? Are they getting rid of the apps that use Dropbox? Got a link about any of this?
Edit: I found this link http://www.youneedabudget.com/blog/post/the-new-ynab-is-here
I'm not sure if I'm interested in paying a yearly fee of $50 ($45 for early adopters) for this new YNAB. I'll probably use YNAB4 until it stops working or until I find another solution. Actually, I'm pretty sure I won't go with the new version of YNAB. I like the current setup that stores all my information in my Dropbox account. That was one of the things that appealed most to me about YNAB4, the fact that they didn't store my data. I like privacy.
I'm looking into Money Manager EX http://www.moneymanagerex.org/ as a replacement for YNAB4. It runs on most platforms, syncs with Dropbox, and has a mobile app too https://play.google.com/store/apps/details?id=com.money.manager.ex . This program is completely free, but I'd donate if it satisfies all my needs that YNAB4 satisfied.
edit2: I installed Money Manager EX on my laptop and on my Android phone. The interface is not as streamlined as the YNAB interface. The mobile app is more streamlined and has a cleaner appearance. I set up a fake bank account and entered some transactions and it all went smooth. Dropbox syncing was flawless.
If you've never used YNAB or another similar app, you might be a little lost with money manager ex, but having used YNAB since February, I feel like it's pretty easy to setup accounts, categories, payees, etc.