First: usually, if you rebuild an index, you get a new set of statistics on the indexed column(s) for free. It'd be silly to read every value, sort it all, and then not use that data to build a new statistics histogram. That's not true if you rebuild a partitioned index. Quoted from the above:
In SQL Server 2012, statistics are not created by scanning all the rows in the table when a partitioned index is created or rebuilt. Instead, the query optimizer uses the default sampling algorithm to generate statistics. To obtain statistics on partitioned indexes by scanning all the rows in the table, use CREATE STATISTICS or UPDATE STATISTICS with the FULLSCAN clause.
That's interesting, but the shocker to me was another tidbit.
When dealing with database integrity errors, I hold my breath while looking at the index ID for problems in an index. Why? Because: Index ID 0 or 1 is raw table data. Index ID 0 is the heap; index ID 1 is the clustered index. (You only ever have one - Index ID of 0 rules out an Index ID of 1, and vice versa.) Index IDs of 2 and higher? They're "just" indexes that can be rebuilt without any risk of data loss.
Ah, but there's a tricky bit now:
In earlier versions of SQL Server, you could sometimes rebuild a nonclustered index to correct inconsistencies caused by hardware failures. In SQL Server 2008 and later, you may still be able to repair such inconsistencies between the index and the clustered index by rebuilding a nonclustered index offline. However, you cannot repair nonclustered index inconsistencies by rebuilding the index online, because the online rebuild mechanism will use the existing nonclustered index as the basis for the rebuild and thus persist the inconsistency. Rebuilding the index offline, by contrast, will force a scan of the clustered index (or heap) and so remove the inconsistency.
So: if you have a damaged index of ID 2 or greater, you have to take it offline to repair it. But don't think about what you're losing - think about what you're gaining! The other option is putting your database in Single User Mode, and running DBCC CHECKDB with REPAIR_REBUILD. So here, you get to take an index offline, instead of taking your whole database offline. It's a fair trade!
Most of the rest of indexing maintenance hasn't changed. If your indexes are under 10% fragmented, great - don't worry about it. Seriously - you can't always get rid of that last bit of fragmentation. For small tables, it might be literally impossible, and for larger ones, there are still probably better places to spend your energy. 10-30% fragmentation is a good time for a defragment/reorganize. If you see more than 30% fragmentation, a rebuild is your best option - but unless you're on Enterprise edition, you can't do an online rebuild so you might want to try to hold off by using a reorganize until you can get a maintenance window.
Oh, one other thing: most of the time you want to leave Fill Factor at the default of 0. A fill factor of 80 means leaving your pages only 80% full. This sounds like a reasonable idea - why pack them full, so that we have page splits as soon as we add a few rows? Why not leave a bit of space so they can fill up over time? It's not a terrible idea, but remember that data pages that are 80% full require 25% more disk space and buffer pool memory to hold them - and thus, 25% more reads and writes to deal with them. If you're having lots of page splits that are slowing you down, sure, consider trying a fill factor on the busiest indexes. But most of the time, you're better off packing them tight, to minimize disk and memory usage, and to reduce the number of reads and writes you need to perform.