SPQR (App Store link) is the swiss army knife of iOS apps for Latinists. It has a plethora of features that make it worth the price tag for any serious student of Latin. In fact, there are so many features, that this post will only cover the core ones in the full name: SPQR Latin Dictionary and Reader.
Dictionaries
SPQR includes Lewis and Short. This seems pretty much the same as the Lewis and Short in Logeion (review of Logeion for iOS here). But SPQR also includes an English-to-Latin dictionary. Here are screenshots of the SPQR dictionaries.


Parsing
Both SPQR and Logeion will get the job done if you know the headword to look up in the dictionary. But if you aren’t sure of the headword (for example if you don’t know to look up stravit under sterno), then you’ll want to use SPQR’s parser (nestled between the two dictionaries on the tab bar under the search field). The parser will give you all the possible forms for a word (e.g. vita might be either nom., voc., or abl. sg. of the noun vita, -ae, or else 2 sg. pres. act. imperative of the noun vito, ‑are.).

Tap the > icon in the Parser results list to see details for each possible headword.

Elsewhere in SPQR is a cool (but almost hidden) feature that allows you to parse whole passages at a time, rather than individual words. Look for the “More” icon and find the feature “Typist.” Paste/type in a passage of Latin (or “Load Example Text” from the action menu [looks like a box with an upward arrow emerging]). Then choose “Parse Text” from the action menu and behold: a neat list of parses for each word in order. The difference between this and the single word parser (apart from doing multiple words at once) is that this will only provide one parse for each word, so if there are multiple possibilities, you won’t see that; you’ll just get one parse per word (apparently the most common of the possibilities). Tapping the action menu again will load your parses up in a draft e-mail.

Typist
Typist (under the “More” icon) is a little notepad that allows easy input of vowels with macrons by putting an extra row of dedicated long vowel keys above the regular keyboard. If you need to type out a lot of Latin with macrons (and do not need formatting), this could be a time-saver. Anything you type here can be copied to the iOS clipboard for pasting into other apps or can be sent directly as an e-mail.
Authors
SPQR comes with a set of Latin texts, including Catullus, Virgil, Caesar, Sallust, and others. Not displayed by default are some Christian Latin texts (Augustine, Bede, Jerome); these can be activated by tapping the cross icon at the top of the Authors screen. Many of these have English translations that you can flip back and forth from with a single tap on the icon of crossed arrows (see image).
Also on the Authors screen is a search field that returns matches from across all the texts. Note that formatting of the text occasionally messes up the results, e.g. searching for lugete did not turn up any matches because in the SPQR text of Catullus III, the word is in all caps (as the first word); it was only found when I searched for lvgete (with v, rather than u).
If you are reading from one of the included texts, you can also easily generate a whole flashcard set from the page you are on without having to add each word, by tapping the icon that looks like cards (see image below).
Selecting a word while reading will bring up the usual iOS contextual menu. If you go all the way to the end of it, you will see an option called “Look up,” which will bring up a window with parsing information and a brief definition. Note that this “Look up” command is not to be confused with the “Define” command that appears earlier in the same menu (“Define” looks up words in the iOS dictionaries that are installed at the system level).

Once you have looked up the word, you can choose to add it to a flashcard list within the app by tapping the button at the bottom of the window.

More about the Flashcards feature in Part 2 of the SPQR coverage.
App Store link: SPQR Latin Dictionary and Reader – Paul Hudson