Short story: When digital seismic receivers arrived on the scene in Calgary in the early 2000s, there was a lot of skepticism. We spent a lot of time comparing them to traditional geophones. The conclusion: they were about the same. Here's one comparison by Michael Hons at CREWES, and here's another; here's yet another from one of the big manufacturers, Sercel (now CGG). Finally, here's a presentation more oriented around earthquake seismology.

Okay, but I was talking about the accelerometers in iPhones!

Oh, sorry. As @Fred points out in his answer, consumer-grade MEMS accelerometers (as you might find in a phone or latop) may not have the sensitivity or calibration that a researcher would want, but one might compensate somewhat for this with multiple measurements, e.g. an array of devices. In other words: quantity, not quality. (This is perfectly legit: we do it in exploration seismics too.)

Dashti et al. (2013) in Earthquake Spectra Journal found you could get useful measurements (e.g. for emergency response) from networks of phones with a few tricks:

• The more measurements the better.
• Horizontal orientation is best.
• Prefer high-friction phone covers.
• Don't expect to get great data for small quakes.
• Treat small groups of phones as arrays.
• Don't use data for phones that fell off a table!