The metric I see most on the internet and on journals' home pages is the 'Impact Factor'. Are there any other metrics that are considered as important as (or more important than) the Impact Factor?
To expand on JeffE's comment, impact factor gets zero respect among mathematicians. It gets very little respect in any field, as far as I know, but it's a particularly bad measure for mathematics journals. For example, it only counts citation received within two years of publication, which is just about the quickest turnaround time you could get in mathematics (given math's publishing practices and timing). So numerically, the impact factor amounts to saying that if your paper doesn't inspire people to drop everything else and rush to get followup work into print quickly enough, then it has had zero impact.
Impact factors are also manipulated by journal editors, often enough to require serious work detecting and punishing this behavior.
The only reason impact factors exist at all is that administrators want simple ways to rate research productivity, especially in dysfunctional settings where there's no infrastructure of trusted experts. Counting citations is easier to defend as "unbiased" than most other approaches.
There are many other numerical measures of journal quality, such as eigenfactors, but they are not popular or widely used.
In 2010, the Australian Research Council rated 20,000 journals by quality based on expert opinion (for example, see here for the math journals). This is still not great, since the ratings miss subtleties (such as journals with greater strength in some subfields than others) and it's not clear how reliable they are for lesser-known journals anyway. However, this is the closest anyone has come to giving a replacement for impact factors based on expert opinion. Unfortunately, it was so much work that they decided not to do it again.
Now the Web of knowledge issues a five-year impact factor that may be considered (slightly) more relevant in some fields, like mathematics. Mathematicians sometimes convince people rating them to use the MathSciNet MCQ instead, which is a five-year impact factor computed with a mostly mathematic database.
The AMS Notices publish yearly a survey of the processing time of many mathematical journals; this is one aspect of the editorial process quality, probably the easiest to measure.
You can find surveys on the prices of journal, which is certainly a good measure of the commercial talent of the publisher.
Overall, quality can mean a lot different things and you should explain for what purpose you intend the measures to be used.