Virtual TI is a popular TI-8x and TI-9x emulator programmed by Rusty Wagner. It has many features, such as screenshots and the ability to link with a calculator over a serial cable.
Version 3.0 is highly limited. It cannot receive files other than Flash applications, and does not emulate the undocumented instructions of the Z80.
LCD controller inaccuracies
This applies to the TI-82/TI-83/TI-83+ series.
Virtual fails to correctly perform 6-bit writes. It keeps the two most significant bits and ORs them to the screen instead of dropping them. The problem is especially noticeable on TI-83 ROM version 1.07, where the V character has a garbage pixel around it.
Virtual TI does not correctly emulate the LCD controller's behavior for going out of bounds. Instead, if the column is ever out of the 0-11 (8-bit) or 0-19 (6-bit) range, the column number is considered invalid until a new column number is written. You can't move the cursor back into valid range to the right or left through LCD writes. However, no programs currently try to access columns which are off the visible screen, so this is not a major problem.
Virtual TI does not emulate the extra 24 pixels of horizontal resolution offered by the LCD controller, which is not visible on the screen. No known programs actually use that feature though.