Is seven inner joins in a query too much?

7 or even more is not at all unusual in data warehouses where a fact table could easily have foreign keys to a dozen dimensions. In the data warehouse scenario, the cardinality of the dimensions is usually low compared to the fact table, so filters on the dimensions help the fact table be utilized through an index seek or scan.

For a normalized transactional schema, it is not usually a problem if the cardinality of the results set is low in the primary base table (i.e. select everything about one customer), because the foreign keys can normally simply result in index seeks or index scans.