Once you've signed in, go to Settings → Notifications and turn off the optional Wishpicks emails you don't want, from Price drop alerts to Product news. Optional emails also have a stop link at the bottom.
Phone notifications? See "Is there a Wishpicks app?".
Steps
Tap your profile picture → Settings → Notifications. In Updates, Notification settings at the top takes you there too.
Turn off what you don't want. Shopping & prices has Price drop alerts and Weekly price recap; Wishlist activity has Gift reservations and Event reminders; News & ideas has Product news. Each switch saves as you flip it.
Turning off Price drop alerts? Tap Turn off alerts to confirm. It changes price tracking as well as emails: see "Why isn't the price on my wish updating?".
Event reminders go to list owners ahead of the list's date, or its anniversary if it has none. Weekly price recap is part of Wishpicks Plus.
Product news starts on outside the EU, EEA, UK and Switzerland. Inside them it starts off, you're asked "Get updates by email?" after adding a few wishes, and moving your country there turns it off.
Why can't I turn off some emails?
Sign-in links, invitations, the welcome email and Wishpicks Plus billing emails always arrive: they're about your account.
Outside the EU, EEA, UK and Switzerland, a few getting-started tips also come in your first days, even with Product news off. They end once your list has a few wishes, or sooner if you tap "Stop tips" in one.
Will I get an email when someone reserves?
Only on lists where you've chosen to see what's reserved: at most once a day, an email says "Something was reserved on your list", but never what or by whom. It's titled "Reservations on" and the list's name, or "Reservations on your wishlists" when it covers several. To see what, open the list ("Can I see what's reserved on my list?"). There's no notice in the app, not even in Updates, and lists made without an account get none.
To stop them, tap Hide at the top of that list, turn off Gift reservations in Settings, or tap "Stop reservation emails" in the email. That link stops only reservation emails.
How do I stop the Keep price tracking emails?
Tap "Stop these reminders" in the email; Settings has no switch for them. That link also stops price-drop alerts and the Weekly price recap, though Settings still shows them on. "Stop price emails" in those emails works the same way.
Will I get emails about gifts I've reserved?
No. Wishpicks doesn't send gifters reminders or news about their reservations. Your reserved gifts are in "Where can I see the gifts I've reserved?".
Tips
Reading one of our emails? Tap "Email settings" at the bottom instead of the stop link: it opens these switches, which you can flip back later. What a stop link turns off can't be undone from Settings.
Want emails in another language? They follow your account's language ("How do I change my language or country?").
Have a list with a birthday or wedding date? Keep Event reminders on: it's your nudge to tidy the list and send its link round again before the day.