Logicmail uses the Bold's (outdated) TLS encryption (see the warning on this page). It still works, but using it is not recommended.
Opera Mini works on cellular data networks without BIS. The work of rendering webpages for Opera Mini is done on Opera's servers, and then the data is compressed and forwarded to the browser. The idea is that this process is supposed to take advantage of off-device processing power and speed up your browsing experience. In practice, it doesn't seem much faster than the built-in browser on the Bold. The system does have a couple of advantages, though: the transmission of compressed information means that Opera Mini uses much less cellular data than a regular browser; and Opera Mini sometimes renders sites that cannot be accessed with the built-in BlackBerry browser due to certificate issues.
UC Browser is another alternative. It works over cellular data without BIS. If you really miss the browser on your old flip phone, you'll feel right at home. Hello Moto! But seriously, if you use it for a bit, you'll come to appreciate its built-in links page and the fact that it notifies you that you're on a wifi or data network.
Alternatively, you can install the Anworm service books to get the built-in browser working over a data connection. See the browser page for more information.
IM+ and IM+ Pro: connect with multiple messenger services, although compatibility is diminishing over time, especially given the device's outdated TLS. These apps no longer work with Skype, Facebook Messenger, or Yahoo Messenger. They do work with Jabber (XMPP) and ICQ if your server doesn't require an up-to-date TLS connection. The unpaid (ad-supported) version has a nasty flaw where it kicks you out of the text-entry box if you receive a message while typing. The paid (ad-free) version does not have this flaw. Both versions tend to disconnect after a while if left running in the background.
Trillian (paid, formerly available at BBW): another app that connects to multiple messenger services. ICQ was reported to work a few years ago.
Google Maps: There are working links for two versions of Google Maps on the introduction page. If you install version 4.5.3 first, you will not be able to accept the terms and conditions, and the app will not finish loading.
The solution is to install version 3.0 first, accept the terms and conditions, and then upgrade to 4.5.3 (this still works in March 2019). Note that you need a cellular data connection to use Google Maps, even without BIS. There is more information here, here and here.
MGMaps (Website) (OTA): Development has stopped and MGMaps was beginning to lose significant functionality as of January 2016. Yahoo and Google maps no longer work, and the search function is broken. Open street maps and windows live maps still worked at that time. There are instructions for downloading maps for offline use here. There's a bit of a learning curve, but it looks like you could have a fairly effective offline map app with it.
If you also use the Google Maps app, it will delete MGMaps! So there's an alternate version that can be installed at the same time as Google Maps.
The developer EOL'd this app with style. It's here (OTA) and he provided a free registration code for everyone: 1943BFF87134
The search feature no longer works. You have to add feed url's manually, but once added, there are all kinds of good features and controls. The alternative is to bookmark podcast feeds in the browser, download episodes, and listen to them with the music player. I prefer having everything organized in the app.
It works as expected, but signing in to your Amazon account might not be a good idea any more. You can convert eBooks to .mobi files and add them manually as well.
The CB Forums app is a version of Tapatalk restricted to the CrackBerry site only.
Tapatalk 220.127.116.11 seems to be finished. The old trick of adding forums with their URLs is no longer working for me. The only way you can keep it working is if you have an existing tapa3.db file. See this post for more information.
RSS Feed Reader:
Opera Mini 8.0 has a built-in RSS reader. Visit the RSS feed in the Opera Mini browser, click on subscribe, and the feed will be added to the 'Feeds' section in your bookmarks.
Join is a generic SIP client, which connects to VOIP services like VOIP.ms and others.
Dell Voice works well for voice only (not texting), and if I remember correctly, works with fongo.com accounts, but not those created via freephoneline.ca. Correct me if I'm wrong.
Facebook and Twitter:
Twitter no longer functions on devices without TLS 1.2.
For Facebook, the app in BB World is just a shortcut to the mobile website. An OTA version is available here.
NewsZ is a web app for Google News RSS feeds. The app permits a choice of three geographic areas (Canada, UK, US) and can be set to render links in mobilized form using the Google Web Light mobilizer.