Elastalert + Kibana + Slack is great if you use logstash/streamstash to aggregate logs internally. I also combine new relic and slack for incident management.
For log aggregation I use Elasticsearch + Logstash + Kibana. For statistics I use Influxdb + Telegraf + Grafana. For service alerts I use Consul + Consul Alerts. Notifications get sent to Pager Duty and/or Slack from one of Kibana, Grafana, or Consul.
The Grafana graphs are especially fun to watch and Kibana has a nice logentries-esque plugin for searching and tailing logs.
It's quite the system to setup but once it's running everything else (i.e. the rest of your app) is much more manageable.
If you're a lone developer (or a small team of developers) isn't a lot better to use something like CloudWatch instead of messing with ELK?
Zabbix(zabbix-slack-alertscript) & StatusCake + Slack
I've gotten really into Slack recently.
I just log everything ye old fashioned way (text files) and then post anything important/noteworthy to a couple of Slack channels.
It's really easy to build custom integrations and Slack is running on all of our devices so as long as we are all subscribed to the relevant channels I can target @channel in my integration and we know straight away if something bad is happening.
I've use the ELK stack on previous projects, it works really well and isn't that difficult to use (there are some great guides on Digital Ocean) and when I get the time I'm going to set it all up for my current project too.
The only thing is you have to host it somewhere, and it's more justifying the budget for that.