5-7% per week.
Paul Graham said it best:
A good growth rate during YC is 5-7% a week. If you can hit 10% a week you're doing exceptionally well. If you can only manage 1%, it's a sign you haven't yet figured out what you're doing.
The best thing to measure the growth rate of is revenue. The next best, for startups that aren't charging initially, is active users. That's a reasonable proxy for revenue growth because whenever the startup does start trying to make money, their revenues will probably be a constant multiple of active users.
First month and year have exponential growth rate because you are starting from 0. You need to average double-digit growth on a monthly basis during your first year. 2nd year the target growth rate YOY should be 300-400%, but also depends on how good the first year was - if the first year was very good your growth rate might slow down, and if first year is spent pivoting then growth should be more aggressive in the 2nd year.
The weekly metric is good for first 3-4 months after launch, but for many businesses there will be some seasonality and growth spikes around major marketing pushes, so monthly or yearly rates are more common.
BUT, growth rate alone doesn't tell the full story - not all metrics are equally important or meaningful. Revenue per customer varies dramatically between B2B and B2C businesses and has a huge impact on overall revenue and profitability.
EDIT: This great article Are you growing fast enough? from Startup Compass has a great chart showing median growth rate of real startups by user base, as well as 90th percentile (about half way into article).