Is there a negative effect if I place an index on every column in a wide table? We have a wide dataset that isn't very tall (say 250K rows, 90 columns). We will be providing users with an interface that allows them to generate arbitrary queries against this dataset. They can select any number of columns, rows; they can filter by, group by, sort by and aggregate by any columns they want.  

This table is actually 'precomputed' from a set of relational tables; this precomputed tables is 90 columns wide and will be used solely for the users' queries. This big flat table will be produced just once a day.

Because we have no idea in advance what they will actually be doing these operations against, we were suggested to place an index on every column of the table.  

My question is, would this have any adverse effects? 

We would also want this 'methodology' to extend to future datasets that we provide similar functionality on; 1.7 million rows with 120 columns

For reference, we are using SQL Server 2008 R2.
It sounds like this is more of a DataWarehouse workload than an OLTP.
In that case, heavily indexed tables are normal. 

Keep in mind a couple of things, when you do your nightly loads, drop the indexes first then reindex after. Also, there will be a higher storage cost but generally this wont be a problem (but be aware of it).

I know your using 2008R2 but FYI, I believe the new columnstore indexes in 2012 shine against this type of workload. If you can't get the performance you want out of 2008R2 consider testing with this index technology on 2012.

Finally, you could monitor the index usage for the first few days/weeks There are missing index scripts and unused index scripts, that can be run on this table once the user query pattern is determined.