Note: I haven't test all of them yet, but I've tested a few.
For RDP, I recommend iTap RDP.
For VNC, I recommend iTeleport.
For SSH, I recommend iSSH.
For proprietary, I recommend LogMeIn Ignition.
For gaming, I recommend everyAir.
I've spent around $100 on remote clients so far. Nothing is more terrible than spending a lot on a program that you just hate.
* iTap RDP (separate RDP and VNC clients), Universal app, $11.99 each.
Pros: Mouse control works similar to iTeleport and LogMeIn (where your entire screen works like a trackpad, giving pixel-perfect control). Nice interface while connected (three-finger tap to open controls, three-finger swipe to bring up keyboard).
Cons: Separate clients for RDP & VNC, no control over mouse-acceleration (note: I have contacted the author, and they said they are looking into adding it).
* Jump Desktop (RDP and VNC), Universal app, $19.99.
Pros: Fastest RDP client I've used, supports both RDP and VNC in one client.
Cons: Shitty mouse control (you inaccurately zoom around and try to tap on what you want to click, or you can use some horrid "push some broken circle around" control). The interface is completely silly. You have the weird "push-circle" control for the upper part of the desktop, but then have to pan everything up to click near the bottom of the desktop. Right-clicking is unpredictable (a two-finger tap ends up with the right-click happening at a different finger than you expect). The controls are basically horrible. This seemed like a big waste of money for how poorly thought-out the entire app was.
* Wyse PocketCloud (RDP and VNC), Universal app, $14.99.
Pros: Interesting "tool box" built into the mouse-pointer.
Cons: Poor mouse control (drag some pointer control around, similar to Jump Desktop).
* iRdesktop (RDP only), Universal app, Free
Cons: Poor mouse control (you have to do a lot of zooming and inaccurately tapping on what you want to click). No real control over the mouse pointer. Is it using a bloody hand print for its icon?
* Mocha (separate RDP and VNC clients), Universal app, $5.99 each
Pros: Lower price than some other clients.
Cons: Poor mouse control (you have to do a lot of zooming and inaccurately tapping on what you want to click). No real control over the mouse pointer.
* iSSH (SSH and VNC), Universal app, $9.99.
Pros: Great SSH client (especially on the iPad). Supports organizing connection entries into folders (a folder for work-related connections, a folder for home-related connections, etc).
Cons: VNC client is almost an after thought. Same poor control as cheap and free clients (you have to do a lot of zooming and inaccurately tapping on what you want to click). Screen is a little cramped on the iPhone & iPod Touch.
* iTeleport (VNC only), $24.99 for Universal app, $19.99 for iPad-only app.
Pros: Great interface (three-finger tap to open controls, three-finger swipe to bring up keyboard). Mouse control works really well (your entire screen is a touchpad, giving pixel-perfect control). It even supports mouse acceleration to speed up the cursor.
Cons: VNC only, a bit pricey (especially considering there are identical iPad and a Universal apps).
* LogMeIn Ignition (proprietary), Universal app, $29.99.
Pros: Lets you manage systems through firewalls. Great control, with both a touchpad control (similar to iTeleport) and a "full screen drag" control where the mouse pointer is fixed and you move the contents around (works especially well on the smaller screens on the iPhone & iPod Touch).
Cons: Costs a LOT, requires special software to be installed on each client you wish to control.
* everyAir (proprietary), Universal app, $4.99/free (promotion).
Pros: Very fast connection. Selectable mouse control makes it easy to maneuver the pointer. Puts an on-screen control for games, such as arrow keys, a joystick-style mouse movement (independent of your regular mouse control), spacebar, etc (makes games like World of Warcraft very playable).
Cons: Requires server software be ran on system. Disables Aero under Windows when ran. May be mostly for games (instead of a general remote desktop app).
* Splashtop (proprietary), iPad and iPhone/iPod app, $1.99 (promotion).
Pros: Very fast connection. Audio is sent to the iOS device.
Cons: Requires server software be installed and ran on system. Poor mouse control.
Clients I haven't tested yet:
Desktop Connect (RDP)
Jaadu / iTeleport RDP (iPhone / iPod Touch only at this time)
With the multiple remote desktop clients I've used, mouse control is usually the most important thing. After all, you interact with your Desktop computer all the time with a mouse, shouldn't a remote desktop app allow you to do mouse-work as well?
Unfortunately, a lot of remote desktop apps have poor mouse control. How do I describe "poor mouse control"? It is anything that makes the mouse inaccurate or hard to use, or requires extra effort to do simple things.
Most remote app control falls into one of three methods:
The best clients I've used (iTap, Jaadu/iTeleport, and LogMeIn) treat the entire screen as a big laptop touchpad/trackpad. You just slide your finger around to move the mouse pointer, align it with something you want to click, and then you tap anywhere on the screen. You have an almost 1x1 pixel accuracy, your finger doesn't block anything you're looking at, and you rarely (if ever) mis-click. A right-click is as simple as a two-finger click. Again, it is always accurate.
Since this is 1x1 pixel accuracy, you can click and control things without zooming at all.
This method also works *great* for controlling a system hooked to an external monitor or TV, as (again) it works as a real touchpad or remote mouse control to the system. You can actually control and click things without even looking at your iOS device.
Another method of control is used in Jump Desktop and Wyse PocketCloud. You basically have a mouse "controller". The pointer stays above your finger and controls similar to how some video games control (Tyrian and Space Invaders Infinity Gene come to mind). This makes it hard to click near the bottom of the screen, and can make it hard to read the screen as your finger may be blocking something you want to see simply because you are trying to move the mouse pointer somewhere.
The control is almost as accurate as Method 1, but with the above limitations that can really annoy. PocketCloud tries to make up for it with their toolbox that adds easy right-clicking and scrolling. Jump Desktop makes no attempt to add any usefulness to this method.
Probably the easiest for developers to implement (as it is seen in pretty much all of the free apps) is the "press somewhere to click". That means you double tap on an icon itself to open it. There is no way to control the mouse pointer, as your finger is always in click mode. Desktop operating systems where NOT designed for touch interfaces, so it can become quite difficult if you treat the Desktop as such, since all the elements are designed for a pixel-perfect mouse pointer. The only way to get any sort of accuracy with this method of control is to Zoom into were you wish to click, try to tap that spot, then zoom back out to see the results of your tap.
After using Method 1, *I* can't stand using anything else.