In your Data View or Data Form web part, you can conditionally display content based on the ddwrt:IfHasRights() function.

<xsl:if test="ddwrt:IfHasRights(permissionMask)">
something...
</xsl:if>

Trying to get info on values for permissionMask from the advanced conditional formatting dialog box was not possible because there is no scrolling of this information in the UI (bug)

After a bit of searching, I found the values in C:\Program Files (x86)\Microsoft Office\Office12\CAML2XSL.XSL

The permissinMask value is the sum of any of the values below:

ViewListItems - 1

AddListItems - 2

EditListItems - 4

DeleteListItems - 8

ApproveItems - 16

OpenItems - 32

ViewVersions - 64

DeleteVersions - 128

CancelCheckout - 256

PersonalViews - 512

ManageLists - 2048

ViewFormPages - 4096

Open - 65536

ViewPages - 131072

AddAndCustomizePages - 262144

ApplyThemeAndBorder - 524288

ApplyStyleSheets - 1048576

ViewUsageData - 2097152

CreateSSCSite - 4194314

ManageSubwebs - 8388608

CreateGroups - 16777216

ManagePermissions - 33554432

BrowseDirectories - 67108864

BrowseUserInfo - 134217728

AddDelPrivateWebParts - 268435456

UpdatePersonalWebParts - 536870912

ManageWeb - 1073741824

UseRemoteAPIs - 137438953472

ManageAlerts - 274877906944

CreateAlerts - 549755813888

EditMyUserInfo - 1099511627776

EnumeratePermissions - 4611686018427387904

FullMask - 9223372036854775807