Preferably a service that offers both a web and native app.
And https://basecamp.com for project management.
They do time tracking and a bunch of other things as well and are continually improving the product.
I did a pretty exhaustive search when I set out to solve this problem a couple years ago, and ended up with a considerable amount of research that I summarized on my blog (https://joshrickert.com/blog/invoicing-apps-for-freelancers/).
I charge a weekly rate (for a variety of reasons that I should probably write down as a blog post), so the data is more for my consumption than for my clients'. Still, knowing how many hours of productivity you can sustainably manage per day is valuable for setting your rates and coming up with estimates.
If Log My Hours is missing a feature you need, reach out and I'll be happy to help :).
* time tracking: a frankenstein combination of system logs (especially helpful when jumping between workstations), paper notebook, and chatlogs
* invoicing: http://billable.me/
* both: some elbow grease
Evolution (and current, w/ a small team):
* time tracking: http://getharvest.com/
* invoicing, accounting, etc: https://www.xero.com/
The first one carried me for a few months, at an average workload of 60~140h/mo and a maintenance workload of about 4 hours total.
The latter is solving somewhat different problems, but does equate to time won on the admin side.
An ACH transfer costs me $0.50. A credit card transaction costs at least 2.9%, although some invoicing tools charge an additional percentage on top of that. On a $4000 invoice that's over $100 I would pay out as fees with another tool.
Nearly every client I've worked with has been okay with paying this way instead of credit card.
I previously used Toggl for time-tracking, but have been transitioning out of hourly billing and haven't been tracking time for months.