I know the mean, SD (or SEM) and sample size for each group. Which tests can I run?

You can enter data as mean, SD (or SEM) and n, and Prism can compute two-way ANOVA. It is not possible to compute repeated measures ANOVA without access to the raw data.

I only know the group means, and don't have the raw data and don't know their SD or SEM. Can I run ANOVA?

Yes, two-way ANOVA is possible if you only have one value for each condition (no subcolumns). In this case, Prism will only be able to compute ordinary (not repeated measures) ANOVA, and will assume that there is no interaction between the row and column factor. It cannot test for interaction without replicates, so simply assumes there is none. This may or may not be a reasonable assumption for your situation

I want to compare three groups. The dependent variable has two possible outcomes. How can I compare the groups?

Not with ANOVA. Enter your data into a contingency table and analyze with a chi-square test.

What does 'two-way' mean?

Two-way ANOVA, also called two-factor ANOVA, determines how a continuous response is affected by two factors. For example, you might measure a response to three different drugs at two time points. The two factors are drug and time.

If you measure response to three different drugs at two time points with subjects from two age ranges, then you have three factors: drug, time and age so wouldwant to choose three-way ANOVA.

What does 'repeated measures' mean? How is it different than 'randomized block'?

The term repeated-measures strictly applies only when you give treatments repeatedly to each subject, and the term randomized block is used when you randomly assign treatments within each group (block) of matched subjects. The analyses are identical for repeated-measures and randomized block experiments, and Prism always uses the term repeated-measures.

What is a mixed-model design?

In the context of two-way ANOVA, a mixed-model is one where one factor is repeated measures and the other is not. Prism can analyze data where neither factor is repeated measures, one of the two factors is repeated measures, or when both factors are repeated measures.  Prism 5 could not analyze data where both factors are repeated measures.

My two factors are genotype and treatment, and each animal was measured at several time points. Can Prism analyze this kind of "two way" ANOVA?

No. Your experimental design has three factors: genotype, treatment and time. If you wanted to use ANOVA, you'd need to use three-way ANOVA.

How does Prism define "cell mean"?

Prism uses the term "cell" to mean the data on one row for one data set. There may be multiple subcolumns side-by-side, so the cell mean is the average of the values in these subcolumns.

How many rows/columns can Prism handle?

Prism cannot run  two-way ANOVA with huge data sets and presents an message telling you so. How huge is huge? Details here.