Model for two way table Suppose you have data in the following format:
               <60 60-69 70-79 80-89 90-99
No Exercise      5   10     2    4    1
Moderate         2   4      12   4    3
Heavy            4   5      18   10   2
Extreme          5   6       7    9   12

The cells represent the number of people who died at that age range. Beside a chi square test, are there any other models that apply here? Would a poisson model be good here? Or could I just run a standard ANOVA? I want to test differences in death at different exercise levels.
 A: 
differences in death at difference exercise levels.

I'm pretty sure you mean differences in age at death.
Chi-square ignores the fact that both set of categories are ordered.
While you could use the middle of each interval as a proxy for age, ANOVA has the problem that these figures won't be normal, and what age would you use for a category like "<60"? Or are you going to code them some other way?
You probably want to check against some kind of location shift, perhaps with ordered alternatives. You might be able to use a Wilcoxon-Mann-Whitney in the first case or a Jonckheere-Terpstra type statistic in the second, but with allowance for the heavy ties (which would require, I suppose, simulating the null distribution of the test statistic, unless you can tolerate the approximation).
A: Ordinal logistic regression with age at death as the response and exercise regime as the predictor would save you having to code the age-ranges as a continuous variable - probably not a good idea with only five categories.
Plotting Kaplan-Meier survival curves & carrying out the log-rank test (an instance of survival analysis) would allow you to account for people who dropped out of the study (there must surely be some if you recruited them at 30 years old) or who are still alive.
