Is there a MySQL maximum database or table count?
Let's look at many perspectives
PERSPECTIVE #1 : SELECTs against MyISAM tables
If you are doing only SELECTs, you need to run this query:
SELECT CONCAT(ROUND(KBS/POWER(1024,
IF(PowerOf1024&lt;0,0,IF(PowerOf1024&gt;3,0,PowerOf1024)))+0.4999),
SUBSTR(' KMG',IF(PowerOf1024&lt;0,0,
IF(PowerOf1024&gt;3,0,PowerOf1024))+1,1))
recommended_key_buffer_size FROM
(SELECT LEAST(POWER(2,32),KBS1) KBS
FROM (SELECT SUM(index_length) KBS1
FROM information_schema.tables
WHERE engine='MyISAM' AND
table_schema NOT IN ('information_schema','mysql')) AA ) A,
(SELECT 2 PowerOf1024) B;

This will recommend the correct size for the MyISAM Key Cache. This maxs at 4GB for 32-bit. You can go higher on 64-bit machines. Yet, use common sense based on the amount of RAM the DB Server has. This should be a concern for you because only the pages from the .MYI are cached. Any thing from the .MYD must be read from disk over and over again.
If the amount of RAM recommended from this query far exceeds the amount of RAM installed by orders of magnitude, just set key_buffer_size to 4G and call it a day on this perspective.
PERSPECTIVE #2 : Leveraging Different Row Formats for MyISAM tables
Altering MyISAM tables to use a FIXED row format can increases overall performance for SELECTs. Why ?
Since CHAR fields require less string manipulation because of fixed field widths, index lookups against CHAR field are on average 20% faster than that of their VARCHAR counterparts. This is not any conjecture on my part.
The book MySQL Database Design and Tuning performed something marvelous on a MyISAM table to prove this. The example in the book did something like the following:
ALTER TABLE tblname ROW_FORMAT=FIXED; 

This directive forces are VARCHARs to have the fixed amount of space allocate like that of a CHAR. I did this at my previous job back in 2007 and took a 300GB table and sped up index lookups by 20%.
Of course, by changing the ROW_FORMAT to FIXED, you will be double the MyISAM table's size in the worst case scenario. If you choose to do this, make sure you have sufficient diskspace.
PERSPECTIVE #3 : Limits on the Number of Open Files from mysqld's vantage point.
Whenever you startup mysqld, many variables are set based on /etc/my.cnf. The rare exception is the option open_files_limit. If my.cnf does not have this setting, mysqld will attempt to compute the best number for this option such that mysqld can still operate and leave whatever files handles available to the OS.
You can set this number higher strictly at your own risk.
PERSPECTIVE #4 : Disk Considerations
Since your storage engine of choice is MyISAM, you must have fast reading disks since data pages are never cached. Please use RAID10 sets. They are easier to do disk maintenances on than other setups. You can could also go with SSD drives. Whatever you choose, prepare for aging disks and periodic disk maintenances. Make sure your RAID cards have the latest firmware upgrades.
SUMMARY
All the information you supplied must be examined from these 4 perspectives. You must strike a good balance and may have to make concessions on your choices based on either budget, available hardware, amount of diskspace, and overall limitations of MyISAM that you have not anticipated.