I've used Track and Share for various general purpose logging reasons; it has built in options for mood etc. but quite customisable to form anything else be it numeric, text or categorical.
Developer is very friendly if you have requests!
If you wanted something with web sync, the nearest I know of is probably Tictrac. I haven't used it much yet, but I understand there is an app that can record entries offline, and then you would use the website for analysis. Originally I was slightly put off because I couldn't see that you could export data you logged onsite, but I believe there was a recent upgrade to enable that so thinking to look again!